Symmetry reductions, exact solutions, and conservation laws of the generalized Zakharov equations

Abstract

In this paper, the generalized Zakharov equations, which describe interactions between high- and low-frequency waves in plasma physics are studied from the perspective of Lie symmetry analysis and conservation laws. Based on some subalgebras of symmetries, several reductions and numerous new exact solutions are obtained. All of these solutions represent modified traveling waves. The obtained solutions include expressions involving Airy functions, Bessel functions, Whittaker functions, and generalized hypergeometric functions. Previously unknown conservation laws are constructed for the generalized Zakharov equations using the direct method. Profiles are presented for some of these new solutions.