Analytic study on bound solitons and soliton collisions for the coupled nonlinear Schrödinger equations

A type of mode-locked fiber laser, which can generate the bound solitons in the anomalous group-velocity dispersion regime, is suggested in this paper via symbolic computation. A transformation is given to convert the coupled nonlinear Schrödinger equations to a simpler form. Analytic two-, three- and N-soliton solutions for the coupled nonlinear Schrödinger equations are obtained. Based on those solutions, formation of the bound solitons is analyzed, and methods for the soliton control are presented. The soliton intensity and collision period can be controlled with the changes in the nonlinearity and group-velocity dispersion of optical fibers. The slight phase shift has a great influence on the bound states of solitons after the soliton collision. To support the results, numerical simulations of three-soliton propagation are performed. Finally, the modulational instability of bound solitons is analyzed.