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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
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
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, 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
Mathematics, Applied
Yu-Jie Feng et al.
Summary: Investigated a (3+1)-dimensional generalized nonlinear evolution equation for shallow-water waves, derived bilinear form, and constructed semi-rational solutions. Analyzed interactions between lumps and solitons. Identified three types of interaction phenomena in higher-order semi-rational solutions influenced by coefficients in the original equation.
APPLICABLE ANALYSIS
(2021)
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)
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, 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
Mathematics, Applied
Xue-Jiao He et al.
Summary: In this study, the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation was investigated using the Hirota bilinear method and symbolic computation. A bilinear Backlund transformation with four equations and five free parameters was constructed, and solutions in Pfaffian, Wronskian, and Grammian forms were derived using determinant properties. Soliton solutions as well as triangle function solutions were also obtained and plotted for specific parameter choices.
ANALYSIS AND MATHEMATICAL PHYSICS
(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
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
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
Peng-Fei Han et al.
Summary: The (3 + 1)-dimensional generalized nonlinear evolution equation was investigated using the Hirota bilinear method, resulting in various types of solutions and their interactions analyzed through symbolic computation. The study revealed the dynamical characteristics of different types of soliton solutions, providing insights for simulating dynamic models. The paper presented some completely new results compared to previous studies.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Mechanical
Dong Wang et al.
Summary: This work focuses on a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation for nonlinear dispersive waves in an inhomogeneous medium. It derives bilinear form and N-soliton solutions, constructs higher-order breather and lump solutions based on these solitons, and investigates the interactions between different types of waves.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Yuan Shen et al.
Summary: This study investigates a (3 + 1)-dimensional generalized nonlinear evolution equation in shallow water waves and obtains X-type, Y-type, and periodic lump-stripe soliton solutions through symbolic computation and the Hirota method. Fusion and fission phenomena are observed in the X-type soliton solutions, while the fission phenomenon is observed in the Y-type soliton solutions. The interaction between periodic lump and stripe solitons is found to be inelastic.
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
Engineering, Mechanical
Yu-Qi Chen et al.
Summary: This paper investigates a (3+1)-dimensional Hirota-Satsuma-Ito-like system for shallow water waves, obtaining a Painleve integrable condition and exploring the propagation characteristics of breathers, kink waves, lump-periodic waves, and solitary waves under certain conditions. The study reveals the periodic changes in height for kink waves and solitary waves during propagation, while the heights of lump-periodic waves remain unchanged.
NONLINEAR DYNAMICS
(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
Cui-Cui Ding et al.
NONLINEAR DYNAMICS
(2019)
Article
Physics, Applied
Hui-Min Yin et al.
MODERN PHYSICS LETTERS B
(2017)
Article
Engineering, Mechanical
Yiren Chen et al.
NONLINEAR DYNAMICS
(2015)
Article
Physics, Multidisciplinary
Mei-Juan Xu et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2015)
Article
Computer Science, Interdisciplinary Applications
Fayssal Benkhaldoun et al.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2013)
