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.
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