Conservation laws and solutions for a nonlinear deformed equation with variable coefficients

Abstract

This paper studies the third-order nonlinear deformed equation with variable coefficients, which is a generalization of CH, DP and DGH equations. Firstly, we investigate its conservation laws for different values of the three variable coefficients in the equation. Thereafter, we find principal Lie algebra of the equation and then find the coefficients that extends the principal Lie algebra. Finally, we present one symmetry reduction case.

Keywords

• Nonlinear deformed equation
• Principal Lie algebra
• Lie symmetries
• Conservation laws