New generalized hyperbolic functions to find new coupled ultraslow optical soliton pairs in a cold three-state double-∧ system

Abstract

We demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schrödinger equations governing the nonlinear evolution of the envelopes probe fields in the four-mixing scheme. Four types of solutions are given explicitly, namely new bright–bright, new dark–dark, new bright–dark and new dark–bright solitons.