Lie symmetries, integrable properties and exact solutions to the variable-coefficient nonlinear evolution equations

DOI10.1007/s11071-017-3566-2zbMath1375.37166OpenAlexW2614390723MaRDI QIDQ1683884

Hanze Liu, Chao Yue

Publication date: 1 December 2017

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-017-3566-2

zbMATH Keywords

symmetryexact solutionBäcklund transformationLax pairintegrable conditioncylindrical KdV types of equationVc-NLEE

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Solutions to PDEs in closed form (35C05) Symmetries of infinite-dimensional dissipative dynamical systems (37L20)

Related Items (20)

Equivalent transformations, bifurcations and exact solutions to a class of variable-coefficient PDE ⋮ Integrable property, Lie symmetry analysis and explicit solutions to the generalized \(\phi^4\) model ⋮ Bifurcations and Traveling Wave Solutions of Lakshmanan–Porsezian–Daniel Equation with Parabolic Law Nonlinearity ⋮ Traveling wave solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity ⋮ An analytic approach to constructing Bäcklund transformations and exact solutions to nonlinear wave equations in non-polynomial form ⋮ Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions ⋮ Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation ⋮ Rational soliton solutions in the nonlocal coupled complex modified Korteweg-de Vries equations ⋮ Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients ⋮ Bilinear forms and solitonic stability for a variable-coefficient Hirota-Satsuma coupled Korteweg-de Vries system in a liquid ⋮ Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms ⋮ Painlevé analysis, group classification and exact solutions to the nonlinear wave equations ⋮ Painlevé test, complete symmetry classifications and exact solutions to R-D types of equations ⋮ Travelling wave solutions of the general regularized long wave equation ⋮ Improved equivalent transformation method for reduction NLPDEs with time-dependent variables ⋮ Semi-rational solutions for the \((2 + 1)\)-dimensional nonlocal Fokas system ⋮ CK transformations, symmetries, exact solutions and conservation laws of the generalized variable-coefficient KdV types of equations ⋮ General Higher-Order Breather and Hybrid Solutions of the Fokas System ⋮ Traveling wave solutions of a generalized Burgers-\(\alpha\beta\) equation ⋮ Rogue waves and hybrid solutions of the Davey-Stewartson I equation

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