Optical dual-waves to a new dual-mode extension of a third order dispersive nonlinear Schrödinger's equation

Abstract

The dual-mode equations refer to nonlinear models that elucidate motion of bi-directional waves traveling simultaneously under the influence of enclosed phase velocity. The initial two-mode model was introduced by Korsunsky, who refined the Korteweg-De Vries equation (KDVe) into a second-order form. In this study, we aim to extend nonlinear Schrödinger equation by restructuring it into a dual-mode format, and subsequently examine the geometric assessment of this new model. The extended exponential function expansion scheme, tanh-coth method, and Kudryashov method are utilized to obtain bi-directional explicit solutions. Additionally, we extensively examine impact of phase velocity on the propagation behavior of these paired waves, utilizing 2D and 3D graphs for analysis. The solutions obtained in this study have significant implications for the propagation of solitons in nonlinear optics. As examined model appears in various applications, all the derived solutions can contribute to the interpretation of the underlying mechanisms behind many nonlinear phenomena in different fields, such as, nonlinear optics, plasma physics, Bose-Einstein condensates, and others.