On invariant analysis and conservation laws for degenerate coupled multi-KdV equations for multiplicity l = 3

TL;DR

This paper analyzes the symmetries and conservation laws of the degenerate coupled multi-KdV equations with multiplicity three, providing classifications and invariant solutions to enhance understanding of related physical phenomena.

Contribution

It offers a full Lie algebra classification and nonlocal conservation laws for the three-field Kaup-Boussinesq equations, advancing symmetry analysis in this context.

Findings

Classification of Lie algebra symmetries for the equations.

Derivation of invariant solutions via optimal group classification.

Identification of nonlocal conservation laws using Ibragimov's theorem.

Abstract

The degenerate coupled multi-KdV equations for coupled multiplicity l=3 are studied. The equations also known as three fields Kaup-Boussinesq equations are considered for invariant analysis and conservation laws. The classical Lie's symmetry method is used to analyze the symmetries of equations. Based on Killing's form which is invariant of adjoint action, the full classification for Lie algebra is presented. Further, one-dimensional optimal group classification is used to obtain invariant solutions. Besides this, using general theorem proved by Ibragimov we find several nonlocal conservation laws for these equations. The conserved currents obtained in this work can be useful for the better understanding of some physical phenomena modeled by the underlying equations.