Conservation laws for self-adjoint first order evolution equations

Abstract

In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using the recent Ibragimov's Theorem on conservation laws, we establish the conservation laws of the equations admiting self-adjoint equations. We illustrate our results applying them to the inviscid Burgers' equation. In particular an infinite number of new symmetries of these equations are found and their corresponding conservation laws are established.

This manuscript has been accepted for publication in Journal of Nonlinear Mathematical Physics

References in corpus (4)

• New results on group classification of nonlinear diffusion-convection equations
• Self-adjoint sub-classes of third and fourth-order evolution equations
• On the paper "Symmetry analysis of wave equation on sphere" by H. Azad and M. T. Mustafa
• Conservations Laws for Critical Kohn-Laplace Equations on the Heisenberg Group

Cited by in corpus (4)

• Group Analysis of the Novikov Equation
• Self-adjoint sub-classes of third and fourth-order evolution equations
• New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order
• Integrability, existence of global solutions and wave breaking criteria for a generalization of the Camassa-Holm equation