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Dynamical behavior near self-similar blowup waves for the generalized b-equation

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 نشر من قبل Weiping Yan Dr
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف W.P. Yan




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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.



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