Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Dynamical stability of the train of smooth solitary waves to the generalized two-component Camassa-Holm system

Authors: Ting Luo and Min Zhu
Journal: Quart. Appl. Math. 75 (2017), 201-230
MSC (2010): Primary 35B35, 35G25
DOI: https://doi.org/10.1090/qam/1453
Published electronically: July 29, 2016
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Abstract: The present study is concerned with the stability of solitary waves for the generalized two-component Camassa-Holm system derived formally as a model in the shallow-water waves. Using the property of almost monotonicity and the local coercivity of the solitary-wave solution, it is shown that the train of $ N$-smooth solitary waves of this system is dynamically stable to perturbations in energy space with a range of parameters.

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Additional Information

Ting Luo
Affiliation: Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408
Email: ting.luo@mavs.uta.edu

Min Zhu
Affiliation: Department of Mathematics, Nanjing Forestry University, Nanjing 310037, People’s Republic of China
Email: zhumin@njfu.edu.cn

DOI: https://doi.org/10.1090/qam/1453
Keywords: Two-component Camassa-Holm system, solitary waves, orbital stability, monotonicity
Received by editor(s): April 14, 2016
Published electronically: July 29, 2016
Article copyright: © Copyright 2016 Brown University

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