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Volume 1, Issue 3
Traveling Wave Solutions of a Fourth-Order Generalized Dispersive and Dissipative Equation

Xiaofeng Li, Fanchao Meng & Zengji Du

DOI: 10.12150/jnma.2019.307

J. Nonl. Mod. Anal., 1 (2019), pp. 307-318.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

Dispersive-dissipative equation, geometric singular perturbation, traveling waves, heteroclinic orbit.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-307, author = {Li , XiaofengMeng , Fanchao and Du , Zengji}, title = {Traveling Wave Solutions of a Fourth-Order Generalized Dispersive and Dissipative Equation}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {3}, pages = {307--318}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.307}, url = {http://global-sci.org/intro/article_detail/jnma/18845.html} }
TY - JOUR T1 - Traveling Wave Solutions of a Fourth-Order Generalized Dispersive and Dissipative Equation AU - Li , Xiaofeng AU - Meng , Fanchao AU - Du , Zengji JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 307 EP - 318 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.307 UR - https://global-sci.org/intro/article_detail/jnma/18845.html KW - Dispersive-dissipative equation, geometric singular perturbation, traveling waves, heteroclinic orbit. AB -

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.

Xiaofeng Li, Fanchao Meng & Zengji Du. (1970). Traveling Wave Solutions of a Fourth-Order Generalized Dispersive and Dissipative Equation. Journal of Nonlinear Modeling and Analysis. 1 (3). 307-318. doi:10.12150/jnma.2019.307
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