Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

Abstract

Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.