Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (1): 243-258.doi: 10.1007/s10473-019-0119-4

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KAM TORI FOR DEFOCUSING KDV-MKDV EQUATION

Wenyan CUI, Lufang MI, Li YIN   

  1. College of Science, Binzhou University, Binzhou 256600, China
  • Received:2017-04-06 Revised:2018-10-15 Online:2019-02-25 Published:2019-03-13
  • Contact: Wenyan CUI E-mail:yufengxingshi@163.com
  • Supported by:
    Supported by NSFC (11601036, 11401041), Science and Technology Foundation of Shandong Province (J16LI52).

Abstract: In this paper, we consider small perturbations of the KdV-mKdV equation
ut=-uxxx + 6uux + 6u2ux
on the real line with periodic boundary conditions. It is shown that the above equation admits a Cantor family of small amplitude quasi-periodic solutions under such perturbations. The proof is based on an abstract infinite dimensional KAM theorem.

Key words: quasi-periodic solution, KdV-mKdV equation, KAM theory, normal form

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