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 - <p style="text-align: justify;">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.</p>