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Mathematics > Analysis of PDEs

arXiv:1804.07664 (math)
[Submitted on 20 Apr 2018]

Title:Dynamics near the solitary waves of the supercritical gKDV Equations

Authors:Jiayin Jin, Zhiwu Lin, Chongchun Zeng
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Abstract:This work is devoted to study the dynamics of the supercritical gKDV equations near solitary waves in the energy space $H^1$. We construct smooth local center-stable, center-unstable and center manifolds near the manifold of solitary waves and give a detailed description of the local dynamics near solitary waves. In particular, the instability is characterized as following: any forward flow not starting from the center-stable manifold will leave a neighborhood of the manifold of solitary waves exponentially fast. Moreover, orbital stability is proved on the center manifold, which implies the uniqueness of the center manifold and the global existence of solutions on it.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.07664 [math.AP]
  (or arXiv:1804.07664v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.07664

Submission history

From: Chongchun Zeng [view email]
[v1] Fri, 20 Apr 2018 15:14:15 UTC (38 KB)
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