Group classification of variable coefficient KdV-like equations

Abstract

The exhaustive group classification of the class of KdV-like equations with time-dependent coefficients $u_t+u{u}_x+g(t)u_{xxx}+h(t)u=0$ is carried out using equivalence based approach. A simple way for the construction of exact solutions of KdV-like equations using equivalence transformations is described.

8 pages; minor misprints are corrected. arXiv admin note: substantial text overlap with arXiv:1104.1981

References in corpus (4)

• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• More common errors in finding exact solutions of nonlinear differential equations. I
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification
• Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach

Cited by in corpus (5)

• Equivalence transformations in the study of integrability
• Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries
• Group analysis of general Burgers-Korteweg-de Vries equations
• Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping
• Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom