On Time-Space Dependent Conservation Laws of Nonlinear Evolution Differential Equations

Abstract

In this paper, we propose an alternative direct algebraic method of constructing, for nonlinear evolution partial differential equations, conservation laws that depend not only on dependent variables and its derivatives but also explicitly on independent variables. As illustration, the fifth order Korteweg de Vries (fKdV) and modified $(n+1)$-dimensional Zakharov-Kuznetvov (ZK) equations are probed.