Conservation laws of the generalized Riemann equations at $N=2,3,4$

Abstract

In this paper, we present infinitely many conserved densities satisfying particular conservation law $F_t=(2uF{)}_x$ for the generalized Riemann equations at $N=2,3,4$. In the $N=2$ case, we also construct conserved densities corresponding to new conservation laws containing an arbitrary smooth function. In virtue of reductions and/or changes of variables, related conserved densities are obtained for two component Hunter-Saxton equation, Hunter-Saxton equation, Gurevich-Zybin equation and Monge-Ampere equation.

14 pages

References in corpus (1)

• Conservation laws and symmetries of Hunter-Saxton equation: revisited