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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
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
Computer Science, Interdisciplinary Applications
Xue-Jiao He et al.
Summary: This paper focuses on constructing the M-lump solution and the Wronskian solution for a (3+1)-dimensional nonlinear model. The M-lump solution is constructed using the long wave limit method, and the three-dimensional plots of different lump solutions are shown as examples. A sufficient condition for the Wronskian solution is given based on the properties of determinant and Plucker relation. Specific examples are also presented.
MATHEMATICS AND COMPUTERS IN 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
Yi-Wei Zhao et al.
Summary: The extended coupled (2+1)-dimensional Burgers system is utilized to describe wave processes in oceanography, acoustics, or hydrodynamics. By employing the Riccati projective equation method and symbolic computation, a variable separation solution is derived. The study focuses on fractal and chaotic structures based on the gradient function (U), and analyzes some excitation properties of the solutions with accompanying figures showing the shape and structure.
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
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
Oriol Guasch et al.
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CHAOS SOLITONS & FRACTALS
(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
Kelsey Frazier et al.
Summary: An investigation was conducted to determine the fractal scaling behavior of the subsurface topography of Arctic sea ice. The study found that young sea ice exhibited fractal scaling geometry parameters, while other types of sea ice did not. This analysis is crucial for predicting the migration of oil spills and future research efforts are recommended.
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
Physics, Multidisciplinary
Xin-Yi Gao et al.
Summary: This paper discusses a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics and presents the similarity reductions based on variable coefficients using symbolic computation.
CHINESE JOURNAL OF PHYSICS
(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
Yu-Hang Yin et al.
Summary: The paper investigates a (3+1)-dimensional nonlinear evolution equation to study features and properties of nonlinear dynamics in higher dimensions. By using the Hirota bilinear method, a bilinear Backlund transformation with six free parameters is constructed, resulting in multiple sets of solutions and new types of interaction solutions. The periodic interaction phenomenon is simulated by setting constraints to the new interaction solution expressed by polynomial-cos-cosh test function.
NONLINEAR DYNAMICS
(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
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
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, 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
Physics, Multidisciplinary
Xin-Yi Gao et al.
Summary: This study focuses on the extended coupled (2+1)-dimensional Burgers system and employs scaling transformation, Bell polynomials, Hirota operators, and symbolic computation to derive two hetero-Ba?cklund transformations. The research also constructs two sets of bilinear forms with one-and two-soliton solutions, which are reliant on coefficients in the original system.
CHINESE JOURNAL OF PHYSICS
(2021)
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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
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
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
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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)
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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.
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Su -Su Chen et al.
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Xin-Yi Gao et al.
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NONLINEAR DYNAMICS
(2021)
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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.
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