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.
