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| Traveling Wave Solutions of a Fourth-order Generalized Dispersive and Dissipative Equation |
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| KeyWord:Dispersive-dissipative equation geometric singular perturbation traveling waves heteroclinic orbit |
| Author Name | Affiliation | | Xiaofeng Li | Department of Mathematics, Xuzhou Vocational Technology Academy of Finance & Economics, Xuzhou, Jiangsu 221008, China
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China | | Fanchao Meng | Department of Mathematics, Xuzhou Vocational Technology Academy of Finance & Economics, Xuzhou, Jiangsu 221008, China | | Zengji Du | School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China |
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| Abstract: |
| 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. |
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