Application of the Composite Variational Principle to Shallow Water Equations

Abstract

In this study, we derive new local conservation laws of the one-layer shallow water equations in the plane flow which are belong to the family of evolution type equations by the composite variational principle of view in the development of the study (N.H. Ibragimov, A new conservation theorem. J. Math. Anal. Appl. 333:311–328, 2007).