Exact solutions and conservation laws of the generalized Schrödinger–Hirota equation

Abstract

In this paper, we consider a nonlinear nonintegrable partial differential equation of the third order, which is a generalization of the Schrödinger–Hirota equation. This equation allows modeling the propagation of optical pulses in a nonlinear medium. We obtained three conservation laws for the equation by direct transformations. For the traveling wave reduction of the generalized Schrödinger–Hirota equation, we found first integrals from the conservation laws. We applied the implicit function method and the simplest equations method to construct optical solitons and exact solutions in the form of periodic waves.