Coupled sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in magneto-optic waveguides with quadratic-cubic nonlinearity

Abstract

The current paper is dedicated to the study of the propagation of progressive solitons in magneto-optical waveguides that carry the quartic-cubic nonlinearity described by a coupled system of of nonlinear Schrödinger equations. In this direction, we take the help of a modified F-expansion method which allows us to widen the class of solutions to these coupled equations and permit the propagation of different waves in the two channels. First of all, we constructed the solutions in terms of Jacobi elliptic functions in the forms of dn−sn, dn−cn, and cn − sn. After that, we obtained the progressive soliton solutions when these functions approached their limiting values with regards to the modulus of ellipticity. The progressive solutions include bright-dark soliton, bright-bright soliton, dark-dark soliton, bright-front soliton, dark-front soliton. In addition, we present the Figures 1-6 which graphically exhibit the representative structures of each explicit solution for some special parameter values.

Modulational instability, modulated wave, and optical solitons for a generalized highly dispersive cubic-quintic-septic-nonic medium with self-frequency shift and self-steepening nonlinear terms

“…A large number of Jacobi elliptic functions, mathematics solutions of the analog of equation ( 21), can be found in the appendix of [103,104] they can then be used to construct the solutions of equation (2), via their expressions equations ( 23), ( 25), (27), and (31). We will only focus on the following physically realistic cases cn dn , and sn.…”