Novel multi-wave solutions for the fractional order dual-mode nonlinear Schr¨odinger equation

Abstract

This paper considers the fractional order dual-mode nonlinear Schr¨odinger equation (FDMNLSE)
with cubic law nonlinearity. This model dissects the absorption or enlargement of dual waves in the occurrence of nonlinearity and distribution influences. Also, it has many implementations in fiber optics and nonlinear physics. This work gives the fractional derivative in terms of time and space conformable sense. We will analyze the periodic cross-kink wave solutions strategy, M-shaped rational solitons technique, M-shaped with one and two kinks procedure, the interaction between periodic and M-shaped method, interaction with M-shaped, I-kink, and rogue wave approach, and their applications for this equation are obtained using logarithmic transformation. The analytical outcomes are analyzed by the graphical illustration displaying the suggested techniques’ reliability and virtue.