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Article
Physics, Multidisciplinary
F. G. Mitri
Summary: In this study, the longitudinal acousto-elastic radiation force exerted on a cylindrical fluid-filled inclusion in an unbounded elastic matrix is derived in the framework of linear elasticity. The analysis provides an exact formalism using partial-waves series and reveals the influence of mode conversion and elastic resonances.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
A. A. Avramenko et al.
Summary: This paper focuses on the theoretical study of fluid flow and heat transfer of Eyring-Powell fluid in a boundary layer over a flat surface. Symmetry transformations were obtained for the full rheological law of Eyring-Powell fluid, leading to self-similar forms of nonlinear differential equations different from the classical Blasius forms. These equations accurately describe the transition from the velocity profiles for a Newtonian fluid to linear profiles for Eyring-Powell fluid.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Yuan Shen et al.
Summary: This study investigates a (2+1)-dimensional generalized Kadomtsev-Petviashvili system via symbolic computation and derives a bilinear auto-Backlund transformation and soliton solutions using the Hirota method. Additionally, periodic wave solutions are obtained using the Hirota-Riemann method. The study also discusses the relationship between periodic-wave and soliton solutions and their approach under a limiting procedure.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: Investigations on electromagnetic-wave/ferromagnetic-material interactions in magneto-optic recording and computer data storage have been conducted. A variable-coefficient modified Kadomtsev-Petviashvili system for certain electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film was studied, with potential applications in magneto-optic recording. Symbolic computation was used to derive auto-Backlund transformations, bilinear forms, and N-solitonic solutions with varying coefficients for electromagnetic waves in ferromagnetic films.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Thermodynamics
Liu-Qing Li et al.
Summary: This paper focused on studying the Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system, which represents nonlinear and dispersive long gravity waves in shallow water. Pfaffian technique was used to construct the Gramian solutions, while asymptotic analysis was applied on two-soliton solutions to explore interaction properties. The study revealed N-soliton solutions with a real function zeta(y) and discussed elastic, inelastic interactions, and soliton resonances for three and four solitons.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2022)
Article
Engineering, Multidisciplinary
Wen-Xiu Ma
Summary: This paper analyzes N-soliton solutions and explores the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations within the Hirota bilinear formulation. An algorithm is proposed to verify the Hirota conditions by factoring out common factors in N wave vectors of the Hirota function and comparing degrees of involved polynomials. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, with proofs of the existence of N-soliton solutions provided for all equations in the two classes.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Mechanical
Dan-Yu Yang et al.
Summary: This study investigates the wave propagation of multiple fields in optical fibers and plasmas. A Lax pair and Darboux transformation are constructed to obtain the solutions of breather and rogue wave. The study finds that the inhomogeneous coefficients affect the characteristics of the breathers and rogue waves.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Tian-Yu Zhou et al.
Summary: This paper investigates a (2+1)-dimensional generalized Burgers system with variable coefficients in a fluid. It obtains the Painleve-integrable constraints of the system with respect to the variable coefficients. Based on truncated Painleve expansions, an auto-Backlund transformation is constructed, along with soliton solutions. Multiple kink solutions are derived using truncated Painleve expansions. Breather solutions, half-periodic kink solutions, and hybrid solutions composed of breathers and kink waves are obtained via complex-conjugate transformation.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Dan-Yu Yang et al.
Summary: In this paper, a three-component coupled derivative nonlinear Schrodinger system is investigated for a certain plasma. Soliton and breather solutions are obtained and their interactions are studied. The modulation instability of plane wave solutions is also examined.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: This article discusses the importance of studying nonlinear optics, fluid mechanics, plasma physics, and atmospheric science. It explores a generalized variable-coefficient Korteweg-de Vries equation and presents the construction of similarity reductions for two sets of wave amplitudes, resulting in known ordinary differential equations. The results are dependent on the variable coefficients in the equation.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2022)
Article
Physics, Multidisciplinary
Liu-Qing Li et al.
Summary: In this paper, a damped variable-coefficient fifth-order modified Korteweg-de Vries equation is investigated for small-amplitude surface waves in a strait or large channel of slowly-varying depth and width with non-vanishing vorticity. Bilinear forms, bilinear Backlund transformation and multi-soliton solutions are derived using the Hirota bilinear method. The effect of alpha(1)(t), beta(t) and gamma(t) on the solutions is discussed analytically and graphically. Various types of solutions, including multi-pole, breather, and hybrid solutions, are obtained.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Applied
Xiao-Tian Gao et al.
Summary: This Letter focuses on the characteristics of water waves in a narrow channel and presents two branches of similarity reductions for the horizontal velocity and elevation of the waves through symbolic computation.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yuan Shen et al.
Summary: This work investigates a (2 + 1)-dimensional Hirota-Satsuma-Ito system that arises in shallow water waves. Using the Hirota method and symbolic computation, certain X-type and resonant Y-type soliton solutions are developed based on the given N-soliton solutions. The study also constructs hybrid solutions consisting of resonant Y-type solitons, solitons, breathers, and lumps. The presented graphics demonstrate the interactions between the resonant Y-type solitons and solitons/breathers/lumps in the respective hybrid solutions. The obtained results are dependent on the water-wave coefficient in the system.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Dan-Yu Yang et al.
Summary: This study investigates an M-coupled variable-coefficient nonlinear Schrödinger system in an optical fiber communication system, and obtains localized wave solutions and explores the interactions between gray solitons and breathers under different conditions.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
He-Yuan Tian et al.
Summary: This paper investigates a three-component coupled nonlinear Schrödinger system and derives new analytical solutions by constructing a Darboux transformation. It is found that on a non-zero-zero-zero background, two kinds of waves can be derived, which are useful for understanding the three-component coupled NLS system. Through asymptotic analysis, more nonlinear wave phenomena are discovered, which are not admitted in traditional NLS equations and two-component coupled NLS systems.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Engineering, Mechanical
Fei-Yan Liu et al.
Summary: In this paper, a (3+1)-dimensional generalized nonlinear evolution equation for shallow water waves is investigated. Nth-order solutions are proved to exist and soliton solutions are constructed. One-periodic-wave solutions are also derived, and the relationship between these solutions is explored. The equation is further simplified to a two-dimensional dynamic system, and the phase portraits of the system are given based on a qualitative analysis.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Yuan Shen et al.
Summary: In this paper, we investigate a (3+1)-dimensional shallow water wave equation with time-dependent coefficients and obtain various solutions and their associated nonlinear phenomena using the Hirota method and symbolic computation.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Xin-Yi Gao et al.
Summary: This paper investigates a variable-coefficient nonlinear dispersive-wave system modeling long gravity water waves in a shallow oceanic environment. Through symbolic computation, the authors perform Painleve analysis and obtain bilinear forms, soliton solutions, and similarity reductions for the system. They also provide graphical discussions on these soliton solutions. The findings of this paper could be useful for future oceanic studies.
WAVES IN RANDOM AND COMPLEX MEDIA
(2022)
Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: Burgers-type equations are widely used in various fields, and our symbolic computation has provided an auto-Backlund transformation and two sets of similarity reductions.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Physics, Applied
Xi-Hu Wu et al.
Summary: This paper investigates an N-coupled high-order nonlinear Schrodinger system using the Darboux transformation method and asymptotic analysis to study the properties of ultrashort optical pulses in an optical fiber. Different-order soliton solutions and their characteristics under various backgrounds are derived and analyzed.
MODERN PHYSICS LETTERS B
(2022)
Article
Mathematics, Applied
Fei-Yan Liu et al.
Summary: This Letter investigates a higher-order BB system for modeling shallow water waves. The Lie group method is used to obtain the symmetry generators, symmetry groups, and symmetry reductions of the system. Hyperbolic-function, trigonometric-function, and rational solutions are derived.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Meng Wang et al.
Summary: This study investigates the ultrashort optical pulses in a birefringent optical fiber through solving a coupled fourth-order nonlinear Schrödinger system. Soliton interactions, polarizations changes with beta value variations, and other nonlinear effects are analyzed and graphically displayed in the research.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Cui-Cui Ding et al.
Summary: This paper investigates a two-component AB system describing wave-packets in a baroclinic fluid. Bright one- and two-soliton solutions are constructed, and the effects of coefficients on the wave packets are analyzed, revealing the interactions between different types of solitons.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Fei-Yan Liu et al.
Summary: This paper investigates the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics. Nth-order Pfaffian solutions are constructed and proved using the modified Pfaffian technique. The study demonstrates the effects of variable coefficients on solitons and presents hybrid solutions composed of breathers, lumps, and solitons.
CHAOS SOLITONS & FRACTALS
(2021)
Editorial Material
Mathematics, Interdisciplinary Applications
Xiao-Tian Gao et al.
Summary: The paper investigates a generalized (2 + 1)-dimensional dispersive long-wave system for nonlinear and dispersive long gravity waves in shallow water, deriving multiple similarity reductions using symbolic computation which each correspond to a known ordinary differential equation. The results are dependent on the constant coefficients in the original system.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Meng Wang et al.
Summary: In this paper, the matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain is studied, and the first-, second- and third-order vector breathers are derived using the generalized Darboux transformation method. The propagation of the first- and second-order vector breathers is shown, along with an analysis of the influence of higher-order linear and nonlinear effects on them. The results depend on the strength of the higher-order linear and nonlinear effects in the equation.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Yong-Xin Ma et al.
Summary: This paper investigates a (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation in fluid dynamics, and provides various soliton and breather-wave solutions through techniques like Hirota method and symbolic computation. It examines the elastic interactions and propagation characteristics of the waves, presenting findings on the unchanged shapes during propagation.
CHINESE JOURNAL OF PHYSICS
(2021)
Article
Physics, Applied
Cong-Cong Hu et al.
Summary: This paper investigates a (3+1)-dimensional Yu-Toda-Sasa-Fukuyama equation for interfacial waves in two-layer liquids or elastic quasiplane waves in lattices. Rational solutions and semi-rational solutions are derived via Kadomtsev-Petviashvili hierarchy reduction. Various types of lump waves and interactions between them are observed, such as fusion between a lump wave and a bell-type soliton and fission of a bell-type soliton.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Materials Science, Multidisciplinary
Bang-Qing Li et al.
Summary: New analytical rogue wave solutions for the KMM system in ferrites are derived using the truncated Painleve' method in this work. It is found that amplitude and frequency parameters play crucial roles in the oscillation of rogue waves, which can be separated into two symmetric ones by adjusting the amplitude parameter or divided into many peaks and troughs by changing the frequency parameter. The amplitude and frequency parameters are highly sensitive to the oscillation of rogue waves, as illustrated by a series of figures and data.
JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS
(2021)
Article
Mathematics, Applied
Xin-Yi Gao et al.
Summary: Recent progress in optical fibers has led to various applications in fields such as nonlinear Schrodinger-type models and symbolic computation. A study on a three-coupled variable-coefficient nonlinear Schrodinger system has provided valuable insights and analytical solutions for picosecond-pulse attenuation/amplification in multicomponent inhomogeneous optical fibers.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Dan-Yu Yang et al.
Summary: This paper investigates a variable-coefficient coupled Hirota system describing vector optical pulses in an inhomogeneous optical fiber. By constructing a Lax pair and a Darboux transformation, bright-bright soliton, bright-dark soliton, and breather solutions are obtained. Interactions between solitons and the decrease in period of bright-dark solitons under certain conditions are highlighted in the study.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Fei-Yan Liu et al.
Summary: This paper investigates a modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics. Painlevé integrability is explored and soliton-cnoidal and resonant solutions are derived. The equation is reduced to certain symmetry reduction equations via Lie point symmetry generators, leading to hyperbolic function and rational solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Interdisciplinary Applications
Wen-Xiu Ma
Summary: This study focuses on constructing N-soliton solutions within the Hirota bilinear formulation and analyzing the Hirota N-soliton conditions in (2+1)-dimensions. A generalized algorithm for proving the Hirota conditions is presented, along with the introduction of two weight numbers to achieve homogeneity of the related polynomials. An application is developed for a general combined nonlinear equation to provide proof of existence of its N-soliton solutions.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Physics, Applied
Tian-Yu Zhou et al.
Summary: This paper investigates a Sharma-Tasso-Olver-Burgers equation for nonlinear dispersive waves, deriving multiple solutions through auto-Backlund transformations and hetero-Backlund transformations. The influence of the coefficients on the solutions is also discussed in the study of this equation.
MODERN PHYSICS LETTERS B
(2021)
Article
Physics, Applied
Sheng-Nan Guan et al.
Summary: This paper investigates a generalized (2+1)-dimensional Hirota-Satsuma-Ito (GHSI) equation using Lie symmetry approach. The study identifies some symmetries and similarity solutions, demonstrates the nonlinear self-adjointness of the equation, and constructs conservation laws based on Lie point symmetries and nonlinear self-adjointness. Additionally, physically meaningful solutions are illustrated graphically with appropriate parameter choices.
MODERN PHYSICS LETTERS B
(2021)
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: In this study, a combined pKP-BKP equation is introduced by considering a linear combination of the potential KP equation and the BKP equation. It is proven that the combined pKP-BKP equation satisfies the Hirota N-soliton condition and possesses an N-soliton solution. The proof involves comparing degrees of homogeneous polynomials associated with the Hirota function in N wave vectors.
JOURNAL OF GEOMETRY AND PHYSICS
(2021)
Article
Physics, Multidisciplinary
Yuan Shen et al.
Summary: This paper investigates a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation using the Hirota method and symbolic computation to present bilinear auto-Backlund transformation and analytic solutions. Higher-order breather solutions are determined based on existing N-soliton solutions, and periodic-wave solutions are derived using the Hirota-Riemann method. Graphical representations of the second-order breather and periodic waves are explored, providing insights into nonlinear phenomena in fluid mechanics.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Physics, Multidisciplinary
Meng Wang et al.
Summary: This paper investigates a variable-coefficient nonlinear Schrodinger system modeling the attenuation or amplification of pulses in optical fibers. Breather solutions are obtained and the effects of dispersion and nonlinearity coefficients on these breathers are analyzed. The results may offer theoretical support for future research on adjusting vector breathers in optical fibers.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Applied
Yuan Shen et al.
Summary: Researchers investigated water waves and proposed a nonlinear evolution equation, along with soliton solutions. The results depend on the water-wave coefficients in the equation.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
He-Yuan Tian et al.
Summary: The study focuses on a coupled nonlinear Schrodinger system describing two orthogonally polarized pulses in a weakly birefringent fiber, constructing dressing transformation and N-th order breather solutions with positive integers. Analysis of limits between N-th order breather solutions and seed solutions, conditions to distinguish degenerate and nondegenerate cases for first-order breathers, and the possibility of breathers being kink-type. Additionally, derivation of superregular breathers (SRBs) for second-order breathers and the variations of quasi-Akhmediev breathers profiles before and after interaction.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2021)
Article
Mathematics, Applied
Lei Hu et al.
Summary: In this paper, the Pfaffian technique is optimized and the Boiti-Leon-Manna-Pempinelli equation for an irrotational incompressible fluid is investigated, with higher-order hybrid solutions constructed. The characteristics of the breather and lump, as well as the limitations of the hybrid solutions, are presented.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Interdisciplinary Applications
Su -Su Chen et al.
Summary: This paper investigates the propagation of nonlinear Alfven waves in inhomogeneous plasma through a variable-coefficient derivative nonlinear Schrodinger equation. Various properties of Alfven soliton solutions are derived, including width, amplitude, velocity, trajectory, interactions, and collapses. The study provides insights into the behavior of Alfven waves in plasma environments.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Xin-Yi Gao et al.
Summary: This study examines a (2+1)-dimensional generalized variable coefficient Boiti-Leon-Pempinelli system for water waves, and constructs a set of hetero-Backlund transformations and similarity reductions through scaling transformations and symbolic computation. These link the original system to a known generalized variable-coefficient Burgers equation and an ordinary differential equation, respectively, depending on the variable coefficients in the original system.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Applied
Yong-Xin Ma et al.
Summary: This paper investigates a (2+1)-dimensional extended Kadomtsev-Petviashvili II equation in fluid mechanics, deriving breather-wave and lump solutions using various methods, and analyzing the effects of coefficients on them.
MODERN PHYSICS LETTERS B
(2021)
Article
Engineering, Mechanical
Chong-Dong Cheng et al.
Summary: This paper investigates a (3+1)-dimensional Korteweg-de Vries equation in a fluid, obtaining bilinear form, N-soliton solutions, and higher-order breather solutions. The effects of alpha, beta, gamma, and delta on the amplitude of the second-order breather are discussed. Hybrid solutions comprising the breathers and solitons are derived via the N-soliton solutions.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Piotr Rozmej et al.
Summary: The authors claim to have derived an equation generalizing the KdV equation to two space dimensions and obtained a soliton solution, but the derivation is shown to be inconsistent and the results have no relation to the problem under consideration.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Yuan Shen et al.
Summary: The study investigates a generalized equation in two-layer fluids or lattices, obtaining bilinear form and auto-Backlund transformation through symbolic computation. Breather solutions and lump solutions are derived based on the Hirota method and an extended homoclinic test approach. The study shows that the amplitudes of breathers and lumps remain unchanged during propagation, with graphical representation under varying coefficients.
PRAMANA-JOURNAL OF PHYSICS
(2021)
Article
Acoustics
Wen-Xiu Ma et al.
Summary: In this study, soliton solutions for the B-type Kadomtsev-Petviashvili equation are analyzed and the Hirota N-soliton condition is verified within the Hirota bilinear formulation. A weight number is used in an algorithm to check the Hirota condition while transforming the Hirota function in N wave vectors to a homogeneous polynomial. Soliton solutions are presented under general dispersion relations.
Article
Physics, Multidisciplinary
Xin-Yi Gao et al.
Summary: This study aims to model nonlinear and dispersive long gravity waves in two horizontal directions using scaling transformations, Bell polynomials, and symbolic computation. The results obtained include branches of hetero-Backlund transformations, bilinear forms, and N-soliton solutions, emphasizing the reliance on coefficients in the system.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Applied
Meng Wang et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2020)
Article
Mathematics, Applied
Xin Yu et al.
APPLIED MATHEMATICS LETTERS
(2020)
Article
Mathematics, Applied
Meng Wang et al.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2020)
Article
Physics, Multidisciplinary
A. M. Siddiqui et al.
CHINESE JOURNAL OF PHYSICS
(2020)
Article
Physics, Mathematical
Na Xiong et al.
ADVANCES IN MATHEMATICAL PHYSICS
(2020)
Article
Physics, Applied
Dan-Yu Yang et al.
MODERN PHYSICS LETTERS B
(2020)
Article
Engineering, Electrical & Electronic
Wen-Xiu Ma
OPTICAL AND QUANTUM ELECTRONICS
(2020)
Article
Physics, Multidisciplinary
Meng Wang et al.
CHINESE JOURNAL OF PHYSICS
(2019)
Article
Physics, Applied
Lei Hu et al.
MODERN PHYSICS LETTERS B
(2019)
Article
Physics, Multidisciplinary
Meng Wang et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2019)
Article
Mathematics, Applied
Zhongzhou Lan
APPLIED MATHEMATICS LETTERS
(2019)
Article
Mathematics, Applied
Ding Guo et al.
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Guang-Mei Wei et al.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Article
Physics, Multidisciplinary
Li Cheng et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2018)
Article
Physics, Multidisciplinary
Xin Yu et al.
Article
Mathematics, Applied
Zhong-Zhou Lan et al.
APPLIED MATHEMATICS LETTERS
(2016)
Article
Engineering, Marine
Xin-Yi Gao
Article
Physics, Multidisciplinary
WX Ma
