Optical dual-waves for couple of dual-mode nonlinear Schrödinger’s equations

Abstract

The concept of dual-mode equations involves nonlinear models that describe the simultaneous motion of bi-directional waves influenced by enclosed phase velocity. The initial two-mode model, introduced by Korsunsky, refined the Korteweg-De Vries equation (KDVe) into a second-order formulation. In this study, our objective is to extend the nonlinear Schrödinger type equations by restructuring them into a dual-mode format and subsequently exploring the geometric assessment of these novels. These nonlinear Schrödinger equations (NLS) equations encompass Kerr nonlinearity, weak nonlocality, power-law nonlinearity, and diffraction. To obtain explicit solutions for the bi-directional models, we employ various methods, including the extended exponential function expansion scheme, sech method, tanh/coth method and Kudryashov method. Furthermore, we extensively analyze the impact of phase velocity on the propagation behavior of these paired waves using 2D and 3D graphs. The solutions derived in this study have significant implications for understanding the propagation of solitons in the realm of nonlinear optics. As the examined model finds applications in various fields, the obtained solutions contribute to the interpretation of underlying mechanisms behind diverse nonlinear phenomena in areas such as nonlinear optics, plasma physics, Bose-Einstein condensates, and more.