Auto-Bäcklund transformation with the solitons and similarity reductions for a generalized nonlinear shallow water wave equation

DOI10.1007/S12346-024-01034-8zbMATH Open1543.35064MaRDI QIDQ6541976

Publication date: 21 May 2024

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Could not fetch data.

PDEs in connection with fluid mechanics (35Q35) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Solutions to PDEs in closed form (35C05)

Cites Work

Title not available (Why is that?)
Water-wave studies on a (2+1)-dimensional generalized variable-coefficient Boiti-Leon-Pempinelli system
New soliton and periodic wave solutions to the fractional DGH equation describing water waves in a shallow regime
Generalized Darboux transformation and solitons for the Ablowitz-Ladik equation in an electrical lattice
Auto-Bäcklund transformations, Lax pair, bilinear forms and bright solitons for an extended \((3+1)\)-dimensional nonlinear Schrödinger equation in an optical fiber
Considering the shallow water of a wide channel or an open sea through a generalized \((2+1)\)-dimensional dispersive long-wave system
New similarity reductions of the Boussinesq equation
Handbook of Differential Equations
Soliton gas in integrable dispersive hydrodynamics
Rossby waves past the breaking point in zonally dominated turbulence
Bilinear form, bilinear auto-Bäcklund transformation, soliton and half-periodic kink solutions on the non-zero background of a \((3+1)\)-dimensional time-dependent-coefficient Boiti-Leon-Manna-Pempinelli equation
Bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a \((2+1)\)-dimensional shallow water equation with the time-dependent coefficients
Ultra-short optical pulses in a birefringent fiber via a generalized coupled Hirota system with the singular manifold and symbolic computation
The highly nonlinear shallow water equation: local well-posedness, wave breaking data and non-existence of \(sech^2\) solutions
Breather wave solutions for the \((3+1)\)-D generalized shallow water wave equation with variable coefficients
On the oceanic/laky shallow-water dynamics through a Boussinesq-Burgers system
Wave profile, Paul-Painlevé approaches and phase plane analysis to the generalized (3+1)-dimensional shallow water wave model
An extension to direct method of Clarkson and Kruskal and Painlavé analysis for the system of variable coefficient nonlinear partial differential equations
Elastic collision between one lump wave and multiple stripe waves of nonlinear evolution equations
Kinetic analysis and numerical tests of an adaptive car-following model for real-time traffic in its
Theoretical investigations on a variable-coefficient generalized forced-perturbed Korteweg-de Vries-Burgers model for a dilated artery, blood vessel or circulatory system with experimental support
Lump and hybrid solutions for a (3+1)-dimensional Boussinesq-type equation for the gravity waves over a water surface
Lie symmetry analysis, optimal system, symmetry reductions and analytic solutions for a \((2+1)\)-dimensional generalized nonlinear evolution system in a fluid or a plasma
Two-layer-liquid and lattice considerations through a \((3+1)\)-dimensional generalized Yu-Toda-Sasa-Fukuyama system
In the shallow water: auto-Bäcklund, hetero-Bäcklund and scaling transformations via a (2+1)-dimensional generalized Broer-Kaup system
Considering the wave processes in oceanography, acoustics and hydrodynamics by means of an extended coupled (2+1)-dimensional Burgers system
A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations
Similarity reductions on a \((2+1)\)-dimensional variable-coefficient modified Kadomtsev-Petviashvili system describing certain electromagnetic waves in a thin film
Riemann-Hilbert approach, dark solitons and double-pole solutions for Lakshmanan-Porsezian-Daniel equation in an optical fiber, a ferromagnetic spin or a protein

Related Items (15)

In the shallow water: auto-Bäcklund, hetero-Bäcklund and scaling transformations via a (2+1)-dimensional generalized Broer-Kaup system ⋮ Symbolic computation on a (2+1)-dimensional generalized nonlinear evolution system in fluid dynamics, plasma physics, nonlinear optics and quantum mechanics ⋮ Bilinear-form and similarity-reduction visit to a variable-coefficient generalized dispersive water-wave system concerning Acta Mech. 233, 2527 and 233, 2415 ⋮ For the shallow water waves: bilinear-form and similarity-reduction studies on a Boussinesq-Burgers system ⋮ Double-pole dark-bright mixed solitons for a three-wave-resonant-interaction system ⋮ \(N\)-soliton and other analytic solutions for a \((3 + 1)\)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation with the time-dependent coefficients for the shallow water waves ⋮ In plasma physics and fluid dynamics: symbolic computation on a \((2+1)\)-dimensional variable-coefficient Sawada-Kotera system ⋮ Modulation instability, bifurcation and chaotic behaviors for a generalized \((2+1)\)-dimensional nonlinear wave equation in a fluid or solid ⋮ Bilinear form, \(N\) solitons, breathers and periodic waves for a (3+1)-dimensional Korteweg-de Vries equation with the time-dependent coefficients in a fluid ⋮ Properties of the hybrid solutions for a generalized \((3 + 1)\)-dimensional KP equation ⋮ Stochastic soliton and rogue wave solutions of the nonlinear Schrödinger equation with white Gaussian noise ⋮ \(\overline{\partial}\)-dressing approach and \(N\)-soliton solutions of the general reverse-space nonlocal nonlinear Schrödinger equation ⋮ Multi-geometric discrete spectral problem with several pairs of zeros for Sasa-Satsuma equation ⋮ In a river or an ocean: similarity-reduction work on a \((3+1)\)-dimensional extended shallow water wave equation ⋮ Conservation laws for a perturbed resonant nonlinear Schrödinger equation in quantum fluid dynamics and quantum optics

This page was built for publication: Auto-Bäcklund transformation with the solitons and similarity reductions for a generalized nonlinear shallow water wave equation

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6541976)