Conservation laws of the generalized short pulse equation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11301012 and 11271363), the Excellent Young Teachers Program of North China University of Technology (Grant No. 14058) and the Doctoral Fund of North China University of Technology (Grant No. 41).

Abstract

We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution. Moreover, any adjoint symmetry is a differential substitution of nonlinear self-adjointness, and vice versa. Consequently, the general conservation law formula is constructed and new conservation laws for some special cases are found.