Acta Mathematica Scientia

, Volume 39, Issue 1, pp 243–258 | Cite as

Kam Tori for Defocusing Kdv-Mkdv Equation

  • Wenyan Cui (崔文艳)
  • Lufang Mi (弭鲁芳)
  • Li Yin (尹枥)


In this paper, we consider small perturbations of the KdV-mKdV equation
$${u_t} = - {u_{xxx}} + 6u{u_x} + 6{u^2}{u_x}$$
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 

2010 MR Subject Classification

37K55 35Q53 


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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  • Wenyan Cui (崔文艳)
    • 1
  • Lufang Mi (弭鲁芳)
    • 1
  • Li Yin (尹枥)
    • 1
  1. 1.College of ScienceBinzhou UniversityBinzhouChina

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