Contact equivalence problem for KDV-type equations
Mostafa Hesamiarshad, Mehdi Nadjafikhah
TL;DR
This paper applies Cartan's method and moving coframe techniques to analyze the contact equivalence problem for KDV-type equations, identifying invariants and conditions for their equivalence under contact transformations.
Contribution
It introduces a systematic approach to classify KDV-type equations using differential invariants and structure equations, advancing the understanding of their symmetry properties.
Findings
Derived structure equations for KDV-type equations.
Identified differential invariants under contact transformations.
Established criteria for local equivalence of these equations.
Abstract
The Cartan's method of equivalence and moving coframe method has been applied to solve the local equivalence problem for KDV-type equations under the action of a pseudo-group of contact transformations. The structure equations, the sets of differential invariants for symmetry groups and equivalent conditions of these equations are found.
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Taxonomy
TopicsContact Mechanics and Variational Inequalities · Vibration and Dynamic Analysis · Differential Equations and Numerical Methods