Solitonic attractors in the coupled nonlinear Schrödinger equations with weak dissipations

Abstract

Abstract We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation. Our study reveals that the two-component soliton solutions act as fixed-point attractors, where the numerical evolution of the system always converges to a soliton solution, regardless of the initial conditions. Interestingly, the fixed-point attractor appears as a soliton solution with a constant sum of the two-component intensities and a fixed soliton velocity, but each component soliton does not exhibit the attractor feature if the dissipation terms are identical. This suggests that one soliton attractor in the coupled systems can correspond to a group of soliton solutions, which is different from scalar cases. Our findings could inspire further discussions on dissipative-soliton dynamics in coupled systems.