The Klein-Gordon-Zakharov equations with the positive fractional power terms and their exact solutions

TL;DR

This paper generalizes the Klein-Gordon-Zakharov equations with positive fractional power terms and derives exact solutions including solitary and sinusoidal waves using subsidiary ODEs.

Contribution

It introduces a new class of generalized Klein-Gordon-Zakharov equations with fractional powers and provides a method to find their exact solutions.

Findings

Derived exact bell-type solitary wave solutions

Obtained algebraic and kink-type solitary wave solutions

Identified sinusoidal traveling wave solutions

Abstract

In this paper, the famous Klein-Gordon-Zakharov equations are firstly generalized, the new special types of Klein-Gordon-Zakharov equations with the positive fractional power terms (gKGZE) are presented. In order to derive the exact solutions of new special gKGZE, the subsidiary higher order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aids of the Sub-ODE, the exact solutions of three special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.