Wave solutions to the Landau-Ginzburg-Higgs equation and the modified KdV-Zakharov-Kuznetsov equation by the Riccati-Bernoulli sub-ODE method

Abstract

In this paper, exact traveling wave solutions of the (1+1)-dimensional Landau-Ginzburg-Higgs equation and the (3+1)-dimensional modified KdV-Zakharov-Kuznetsov equation, which are the partial differential equations for ion wave equations, are extracted using the Riccati-Bernoulli sub-ODE method. The obtained solutions are shown by hyperbolic and trigonometric functions, which can be transformed into kink waves and periodic waves in their physical nature.