Traveling waves in a generalized nonlinear dispersive–dissipative equation |
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| Authors: | Xiaohui Shang Zengji Du |
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| Affiliation: | School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, China |
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| Abstract: | D. Zeidan In this paper, we consider the existence of traveling waves in a generalized nonlinear dispersive–dissipative equation, which is found in many areas of application including waves in a thermoconvective liquid layer and nonlinear electromagnetic waves. By using the theory of dynamical systems, specifically based on geometric singular perturbation theory and invariant manifold theory, Fredholm theory, and the linear chain trick, we construct a locally invariant manifold for the associated traveling wave equation and use this invariant manifold to obtain the traveling waves for the nonlinear dispersive–dissipative equation. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | traveling waves dispersive– dissipative equation geometric singular perturbation theory invariant manifold heteroclinic orbits |
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