J. Nonl. Mod. Anal., 1 (2019), pp. 307-318.
Published online: 2021-04
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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.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.307}, url = {http://global-sci.org/intro/article_detail/jnma/18845.html} }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.