Abstract: 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 homoclinic orbits is further confirmed.Ultimately,it is demonstrated that,under specific parameter conditions,the subcritical quintic Ginzburg-Landau equation with slow diffusion exhibits pulse solutions.

Key words: quintic real Ginzburg-Landau equation, pulse solution, geometric perturbation, homoclinic orbit, Melnikov function