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Mathematical Physics

arXiv:1804.02285 (math-ph)
[Submitted on 5 Apr 2018 (v1), last revised 5 Oct 2018 (this version, v3)]

Title:Nonlinear stability of higher order mKdV breathers

Authors:Miguel A. Alejo, Eleomar Cardoso
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Abstract:We are interested in stability results for breather solutions of the 5th, 7th and 9th order mKdV equations. We show that these higher order mKdV breathers are stable in $H^2(\R)$, in the same way as \emph{classical} mKdV breathers. We also show that breather solutions of the 5th, 7th and 9th order mKdV equations satisfy the same stationary fourth order nonlinear elliptic equation as the mKdV breather, independently of the order, 5th, 7th or 9th, considered.
Comments: 14 pages. This is v3
Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
MSC classes: Primary 37K15, 35Q53, Secondary 35Q51, 37K10
Cite as: arXiv:1804.02285 [math-ph]
  (or arXiv:1804.02285v3 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1804.02285

Submission history

From: Miguel Angel Alejo Plana [view email]
[v1] Thu, 5 Apr 2018 10:50:39 UTC (36 KB)
[v2] Mon, 9 Apr 2018 08:57:43 UTC (37 KB)
[v3] Fri, 5 Oct 2018 11:33:14 UTC (43 KB)
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