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Type: Journal article
Title: Existence, uniqueness, and analyticity of space-periodic solutions to the regularized long-wave equation
Author: Chertovskih, R.
Chian, A.-L.
Podvigina, O.
Rempel, E.
Zheligovsky, V.
Citation: Advances in Differential Equations, 2014; 19(7-8):725-754
Publisher: Khayyam Publishing
Issue Date: 2014
ISSN: 1079-9389
Statement of
R. Chertovskih, A.C.L. Chian, O. Podvigina, E.L. Rempel, and V. Zheligovsky
Abstract: We consider space-periodic evolutionary and travelling-wave solutions to the regularized long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.
Rights: Copyright status unknown
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