Propagation of two-wave solitons depending on phase-velocity parameters of two higher-dimensional dual-mode models in nonlinear physics

Abstract

Nonlinear evolution equations exhibit a variety of physical behaviours, which are clearly illustrated by their exact solutions. In this view, this article is concerned with the study of dual-mode (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) and Zakharov-Kuznetsov (ZK) equations. These models describe the propagation of two-wave solitons traveling simultaneously in the same direction and with mutual interaction dependent on an embedded phase-velocity parameter. The considered nonlinear evolution equations have been solved analytically for the first time using the Paul-Painlevé approach method. As a result, new abundant analytic solutions have been derived successfully for both the considered equations. The 3D dynamics of each of the solution has been plotted by opting suitable constant values. These graphs show the dark-soliton, bright-soliton, complex dual-mode bright-soliton and complex dual-mode dark-soliton solutions.