Some New Optical Waves Interactions Via Modified Jacobi Elliptic Functions Method

Abstract

This article explains how long and short waves influence each other within a highly complex nonlinear structure when there is a detuning factor involved. The explanation is based on the nonlinear complex Benney system, and we first consider this system before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on theinteraction between long and short waves in highly complex nonlinear system. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.