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Traveling waves in a generalized nonlinear dispersive–dissipative equation
Author(s) -
Shang Xiaohui,
Du Zengji
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3750
Subject(s) - dissipative system , mathematics , nonlinear system , center manifold , invariant manifold , mathematical analysis , invariant (physics) , manifold (fluid mechanics) , dispersive partial differential equation , traveling wave , classical mechanics , partial differential equation , mathematical physics , physics , quantum mechanics , engineering , bifurcation , mechanical engineering , hopf bifurcation
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.