Existence of Pulse Solutions for the Quintic Real Ginzburg-Landau Equation with Coupled Slow Diffusion Mode
Utilizing Fenichel's geometric singular perturbation theory,we transform the problem of pulse solution existence for a coupled subcritical quintic real Ginzburg-Landau equation with slow diffusion mode into a geometric perturbation scenario,showing the transversality between critical manifolds.Through the computation of the Melnikov function's zeros on the critical manifolds,the presence of ho-moclinic orbits is further confirmed.Ultimately,it is demonstrated that,under specific parameter condi-tions,the subcritical quintic Ginzburg-Landau equation with slow diffusion exhibits pulse solutions.
quintic real Ginzburg-Landau equationpulse solutiongeometric perturbationhomoclinic or-bitMelnikov function
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