Exact solutions for the generalized KdV equation by using Bäcklund transformations

DOI10.1016/j.jfranklin.2011.04.013zbMath1231.35219OpenAlexW1966081763MaRDI QIDQ658579

Hassan A. Zedan

Publication date: 13 January 2012

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2011.04.013

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (9)

The application of the homotopy analysis method and the homotopy perturbation method to the Davey-Stewartson equations and comparison between them and exact solutions ⋮ Invariance of the nonlinear generalized NLS equation under the Lie group of scaling transformations ⋮ Lie groups analysis and contact transformations for Itô system ⋮ The application of the homotopy perturbation method and the homotopy analysis method to the generalized Zakharov equations ⋮ Exact solutions to Euler equation and Navier-Stokes equation ⋮ A novel class of solutions for the \((2+1)\)-dimensional higher-order Broer-Kaup system ⋮ Elementary functions for constructing exact solutions to nonlinear partial differential equations with applications to nonlinear Schrödinger type and MHD equations ⋮ Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations ⋮ Exact multi-wave solutions for the KdV equation

Cites Work

• Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear Euler equations
• A New Integrable Nonlinear Evolution Equation
• Cusp Soliton of a New Integrable Nonlinear Evolution Equation
• Simple Derivation of Backlund Transformation from Riccati Form of Inverse Method
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited
• Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation
• The homogeneous balance method, Lax pair, Hirota transformation and a general fifth-order KdV equation

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