Traveling Wave Solutions of a Fourth-Order Generalized Dispersive and Dissipative Equation (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider a generalized nonlinear forth-order dispersive-dissipative equation with a nonlocal strong generic delay kernel, which describes wave propagation in generalized nonlinear dispersive, dissipation and quadratic diffusion media. By using geometric singular perturbation theory and Fredholm alternative theory, we get a locally invariant manifold and use fast-slow system to construct the desire heteroclinic orbit. Furthermore, we construct a traveling wave solution for the nonlinear equation. Some known results in the literature are generalized.
Keywords: Dispersive-dissipative equation; geometric singular perturbation; traveling waves; heteroclinic orbit.