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 Ft=(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.
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