Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations

Abstract

We classify the admissible transformations in a class of variable coefficient Korteweg--de Vries equations. As a result, full description of the structure of the equivalence groupoid of the class is given. The class under study is partitioned into six disjoint normalized subclasses. The widest possible equivalence group for each subclass is found which appears to be generalized extended in five cases. Ways for improvement of transformational properties of the subclasses are proposed using gaugings of arbitrary elements and mapping between classes. The group classification of one of the subclasses is carried out as an illustrative example.

15 pages; minor corrrections

References in corpus (4)

• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Algebraic method for finding equivalence groups
• Conservation Laws of Variable Coefficient Diffusion-Convection Equations
• Equivalence groupoid of generalized potential Burgers equations

Cited by in corpus (5)

• Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
• Extended symmetry analysis of generalized Burgers equations
• Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
• Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
• Mapping method of group classification