Related references
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Article
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Long-Xing Li
Summary: A (3+1)-dimensional generalized shallow water waves equation is investigated using different methods. N-soliton solutions, T-breathers, rogue waves, and M-lump solutions are derived through degeneration and parameter limit methods. Furthermore, hybrid solutions composed of soliton, breather, and lump are found during the partial degeneration process of N-soliton.
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Article
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Article
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Summary: In this Letter, we investigate an extended (3+1)-dimensional nonlinear Schrodinger equation in an optical fiber. The auto-Backlund transformations and a Lax pair are obtained under certain optical-fiber coefficient constraints. Bilinear forms, bright two-soliton, and bright three-soliton solutions are derived using the Hirota method under certain optical-fiber coefficient constraints.
APPLIED MATHEMATICS LETTERS
(2022)
Article
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Usman Younas et al.
Summary: In this article, the wave behavior of a (3+1)-dimensional dynamical nonlinear model that models shallow water waves is discussed. The Hirota bilinear method is employed to secure the diversity of wave structures, and various types of solutions are extracted. The findings of this research enhance the understanding of nonlinear dynamical behavior and demonstrate the efficacy of the employed methodology.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
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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.
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Article
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Yuan Shen et al.
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APPLIED MATHEMATICS LETTERS
(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
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.
