Higher order conservation laws of the Caudery-Dodd-Gibbon-Sawada-Kotera equation by scaling method

In this paper, a novel conservation law for the Caudrey-Dodd-Gibon-Sawada-Kotera equation utilizing scaling method is derived. This approach is systematic and relies on variational calculus and linear algebra. Also, the conservation law's density is developed by examining the scaling symmetry of the equation, while the corresponding flux is determined through the homotopy operator. This density-flux combination yields a conservation law for the equation. In particular, we establish a conservation law of rank $8$ for the Caudrey-Dodd-Gibon-Sawada-Kotera equation.