Stability analysis for moving dissipative solitons in two-dimensional dynamical model

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Pulse propagating in inhomogeneous nonlinear media with linear/nonlinear gain and loss described by the asymmetrical (2 + 1)-dimensional cubic-quintic Ginzburg-Landau equation is considered. The evolution and the stability of the dissipative optical solitons generated from an asymmetric input with respect to two transverse coordinates x and y are studied. Our approach is based on the variational method. This approach allows us to analyze the influence of various physical parameters on the dynamics of the propagating signal and its relevant parameters. According to the parameters of the system and a suitable choice of the test function, a domain of dissipative parameters for stable solitonic solutions is determined. Bifurcation diagrams related to the existence of the stationary solutions presented show a good agreement between analytical and numerical results.