Interactions among periodic optical solitons for the variable coefficient coupled nonlinear Schrödinger equations

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

“…Because of its importance, many new methods and techniques have been proposed to study the CNLS equation, which include the Bäcklund transformation, the variational iteration method, the extended unified method, and the Hirota method [4][5][6][7][8][9]. However, the study of CNLS equations with variable coefficients [10][11][12][13][14] has more important theoretical significance and practical value than CNLS equations with constant coefficients because it usually describes the inhomogeneous effects of nonlinear optical pulse propa-gations in the real optical fiber communication system. The CNLS equations with variable coefficients are expressed as follows:…”

“…Obviously, the integrability method, the modified sine-Gordon equation method, the unified method, the improved F-expansion method, and the Hirota bilinear method have used to establish the traveling wave solutions of the CNLS equation with variable coefficients in Ref. [10][11][12][13][14], respectively. In this paper, we investigate the dynamical properties and the classification of single traveling wave solutions of the CNLS equation with variable coefficients based on the bifurcation theory and the complete discrimination system method.…”