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

Luo, Ting; Zhu, Min

doi:10.1090/qam/1453

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
MathSciNet review: 3614495
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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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