A SYMMETRY INVARIANCE ANALYSIS OF THE MULTIPLIERS & CONSERVATION LAWS OF THE JAULENT-MIODEK AND SOME FAMILIES OF SYSTEMS OF KdV TYPE EQUATIONS

In this paper, we study and classify the conservation laws of the Jaulent-Miodek equations and other systems of KdV type equations which arises in, inter alia, shallow water equations. The main focus of the paper is the construction of the conservation laws as a consequence of the interplay between symmetry generators and multipliers (integration factors), particularly, the higher-order ones and the significance of the Euler operators for systems of equations.