Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients
DOI10.1007/s12346-023-00813-zzbMath1529.35516OpenAlexW4385636687MaRDI QIDQ6096396
Chunhui Feng, Dan-Yu Yang, Xiao-Tian Gao, Bo Tian
Publication date: 12 September 2023
Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s12346-023-00813-z
symbolic computationbilinear formHirota methodshallow water wavesbilinear Bäcklund transformations\((2+1)\)-dimensional shallow water equation with time-dependent coefficientsbreather and periodic-wave solutions
Symbolic computation and algebraic computation (68W30) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Periodic solutions to PDEs (35B10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08) PDEs in connection with geophysics (35Q86) Geophysical flows (76U60)
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Cites Work
- Unnamed Item
- Multiple kink solutions for two coupled integrable (2+1)-dimensional systems
- One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada-Kotera equation
- Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method
- Periodic, breather and rogue wave solutions for a generalized \((3+1)\)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics
- Water-wave studies on a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system
- Symbolically computing the shallow water via a \((2+1)\)-dimensional generalized modified dispersive water-wave system: similarity reductions, scaling and hetero-Bäcklund transformations
- Darboux transformation, localized waves and conservation laws for an \(M\)-coupled variable-coefficient nonlinear Schrödinger system in an inhomogeneous optical fiber
- Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended \((3+1)\)-dimensional nonlinear Schrödinger equation in an optical fiber
- New type of multiple lump and rogue wave solutions of the \((2+1)\)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili equation
- Considering the shallow water of a wide channel or an open sea through a generalized \((2+1)\)-dimensional dispersive long-wave system
- Bäcklund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation
- Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients
- Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves
- Lie group analysis for a higher-order Boussinesq-Burgers system
- Reflecting upon some electromagnetic waves in a ferromagnetic film via a variable-coefficient modified Kadomtsev-Petviashvili system
- \(N\)-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium
- Nonlinear differential-difference hierarchy relevant to the Ablowitz-Ladik equation: Lax pair, conservation laws, \(N\)-fold Darboux transformation and explicit exact solutions
- Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation
- The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments
- Upscale transfer of waves in one-dimensional rotating shallow water
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