Self-adjointness and conservation laws of Burgers-type equations

Abstract

This paper focuses on the self-adjointness of some Burgers-type equations based on the existing definitions. It follows that the corresponding Frobenius Burgers-type equations are constructed by taking values in a commutative subalgebra [Formula: see text]. In order to investigate the self-adjointness of these Frobenius-type equations, we introduce a few additional notations and definitions. Additionally, the conservation laws are obtained of several equations studied by using symmetries.