New Wave Solutions for the Two-Mode Caudrey–Dodd–Gibbon Equation

Abstract

In this paper, we present new dynamical properties of the two-mode Caudrey–Dodd–Gibbon (TMCDG) equation. This equation describes the propagation of dual waves in the same direction with different phase velocities, dispersion parameters, and nonlinearity. This study takes a full advantage of the Kudryashov method and of the exponential expansion method. For the first time, dual-wave solutions are obtained for arbitrary values of the nonlinearity and dispersive factors. Graphs of the novel solutions are included in order to show the waves’ propagation, as well as the influence of the involved parameters.