Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Abstract

This work concerns the fractional‐order dual‐mode nonlinear Schrödinger equation (FDMNLSE), which portrays the augmentation or absorption of dual waves. This model dissects the concurrent generation of two characteristic waves dealing with dual modes and introduces three physical parameters: nonlinearity, phase velocity, and dispersive factor. In the context of photonics, NLSE models the propagation of soliton pulses over intercontinental distances. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. We analyze the multi‐waves method, homoclinic breather approach, and interactional solution with the double ‐functions procedure, and their applications for this equation are obtained using logarithmic transformation. The multi‐wave method is a well‐known phenomenon in nonlinear science that describes the interaction of three waves that satisfy certain resonance conditions. A breather wave is a localized and oscillatory solution that maintains its shape over time. Finally, we will discuss the dynamics of our newly obtained solutions with the help of graphs by assigning appropriate values to the parameters. The proposed methods are straight and aggressive, so the approved form can be extended for more nonlinear models. The findings are exceptional in comparison to previous findings in the literature. These outcomes may have significance for additional investigation of such frameworks to handle the nonlinear issues in applied sciences. The obtained results help us understand fluid propagation and incompressible fluids.