Dynamical behavior near self-similar blowup waves for the generalized b-equation
Analysis of PDEs
2018-06-19 v1 Dynamical Systems
Abstract
In this paper, we consider the explicit wave-breaking mechanism and its dynamical behavior near this singularity for the generalized b-equation. This generalized b-equation arises from the shallow water theory, which includes the Camassa-Holm equation, the Degasperis-Procesi equation, the Fornberg-Whitham equation, the Korteweg-de Vires equation and the classical b-equation. More precisely, we find that there exists an explicit self-similar blowup solution for the generalized b-equation. Meanwhile, this self-similar blowup solution is asymptotic stability in a parameters domain, but instability in other parameters domain.
Keywords
Cite
@article{arxiv.1806.06391,
title = {Dynamical behavior near self-similar blowup waves for the generalized b-equation},
author = {W. P. Yan},
journal= {arXiv preprint arXiv:1806.06391},
year = {2018}
}
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19 page