Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves
From MaRDI portal
Publication:2236705
DOI10.1016/j.aml.2021.107301zbMath1476.35082OpenAlexW3152777496MaRDI QIDQ2236705
Publication date: 26 October 2021
Published in: Applied Mathematics Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.aml.2021.107301
symbolic computationHirota method\((3+1)\)-dimensional generalized nonlinear evolution equationbilinear auto-Bäcklund transformation
Related Items (35)
Auto-Bäcklund transformation, similarity reductions and solitons of an extended \((2+1)\)-dimensional coupled Burgers system in fluid mechanics ⋮ Bilinear form and nonlinear waves of a \((1+1)\)-dimensional generalized Boussinesq equation for the gravity waves over water surface ⋮ Bilinear auto-Bäcklund transformations and similarity reductions for a \((3+1)\)-dimensional generalized Yu-Toda-Sasa-Fukuyama system in fluid mechanics and lattice dynamics ⋮ Nonlocal symmetry, exact solutions and conservation laws of the \((1+1)\)-dimensional Levi equation ⋮ Considering the shallow water of a wide channel or an open sea through a generalized \((2+1)\)-dimensional dispersive long-wave system ⋮ Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain ⋮ A (2+1)-dimensional modified dispersive water-wave (MDWW) system: Lie symmetry analysis, optimal system and invariant solutions ⋮ Lie group analysis for a higher-order Boussinesq-Burgers system ⋮ On a variable-coefficient AB system in a baroclinic flow: generalized Darboux transformation and non-autonomous localized waves ⋮ Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation ⋮ Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity ⋮ Regarding the shallow water in an ocean via a Whitham-Broer-Kaup-like system: hetero-Bäcklund transformations, bilinear forms and \(M\) solitons ⋮ Elastic two-kink, breather, multiple periodic, hybrid and half-/local-periodic kink solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves ⋮ Mock-integrability and stable solitary vortices ⋮ \(N\)-fold generalized Darboux transformation and soliton interactions for a three-wave resonant interaction system in a weakly nonlinear dispersive medium ⋮ Chimera states under genuine local coupling ⋮ Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects ⋮ Thinking about the oceanic shallow water via a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system ⋮ Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients ⋮ Higher-order breather, lump and hybrid solutions of (2 + 1)-dimensional coupled nonlinear evolution equations with time-dependent coefficients ⋮ Optical solitons of a cubic-quartic nonlinear Schrödinger equation with parabolic law nonlinearity in optical metamaterials ⋮ On the oceanic/laky shallow-water dynamics through a Boussinesq-Burgers system ⋮ Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Solitons, breathers and modulation instability for a higher-order coupled nonlinear Schrödinger system for the ultrashort optical pulses in a nonlinear medium ⋮ Rational and semi‐rational solutions for a (3 + 1)‐dimensional generalized KP–Boussinesq equation in shallow water wave ⋮ Travelling-wave, mixed-lump-kink and mixed-rogue-wave-kink solutions for an extended \((3+1)\)-dimensional shallow water wave equation in oceanography and atmospheric science ⋮ Solitonic fusion and fission for a \((3 + 1)\)-dimensional generalized nonlinear evolution equation arising in the shallow water waves ⋮ Hetero-Bäcklund transformation, bilinear forms and \(N\) solitons for a generalized three-coupled Korteweg-de Vries system ⋮ Certain electromagnetic waves in a ferromagnetic film ⋮ Magnetooptic studies on a ferromagnetic material via an extended \((3+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system ⋮ Novel approximations to a nonplanar nonlinear Schrödinger equation and modeling nonplanar rogue waves/breathers in a complex plasma ⋮ Oceanic shallow-water symbolic computation on a \((2+1)\)-dimensional generalized dispersive long-wave system ⋮ Symbolically computing the shallow water via a \((2+1)\)-dimensional generalized modified dispersive water-wave system: similarity reductions, scaling and hetero-Bäcklund transformations ⋮ Taking into consideration an extended coupled (2+1)-dimensional Burgers system in oceanography, acoustics and hydrodynamics ⋮ Kraenkel-Manna-Merle saturated ferromagnetic system: Darboux transformation and loop-like soliton excitations
Cites Work
- Unnamed Item
- Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method
- On well-posedness of a dispersive system of the Whitham-Boussinesq type
- Method for solving hyperbolic systems with initial data on non-characteristic manifolds with applications to the shallow water wave equations
- Mixed lump-soliton solutions of the \((3+1)\)-dimensional soliton equation
- Fission and fusion collision of high-order lumps and solitons in a \((3+1)\)-dimensional nonlinear evolution equation
- Water-wave symbolic computation for the Earth, Enceladus and Titan: the higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations
- Lax pairs, infinite conservation laws, Darboux transformation, bilinear forms and solitonic interactions for a combined Calogero-Bogoyavlenskii-Schiff-type equation
- New integrable Boussinesq equations of distinct dimensions with diverse variety of soliton solutions
- Solitary-wave and new exact solutions for an extended (3+1)-dimensional Jimbo-Miwa-like equation
- Bilinear form and solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow-water waves
This page was built for publication: Bilinear auto-Bäcklund transformations and soliton solutions of a \((3+1)\)-dimensional generalized nonlinear evolution equation for the shallow water waves