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Quasi-Periodic Solutions for Non-Autonomous mKdV Equation

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Abstract

In this paper, we consider the non-autonomous modified Korteweg-de Vries (mKdV) equation

$${u_t} = {u_{xxx}} - 6f\left( {\omega t} \right){u^2}{u_x},x \in \mathbb{R}/2\pi \mathbb{Z}$$

, where f(ωt) is real analytic and quasi-periodic in t with frequency vector ω = (ω1,ω2, · · ·; ω m ). Basing on an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field, we obtain the existence of Cantor families of smooth quasi-periodic solutions.

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Authors and Affiliations

  1. College of Science, Binzhou University, Binzhou, China

    Wenyan Cui, Lufang Mi & Li Yin

Authors
  1. Wenyan Cui
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  2. Lufang Mi
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  3. Li Yin
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Corresponding author

Correspondence to Lufang Mi.

Additional information

The authors were supported by NSFC 11401041, 11601036, Science Foundations of Binzhou University under grant number BZXYL1704, 2013Y02, and by the Science and Technology Foundations of Shandong Province J14li54, J16LI52.

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Cui, W., Mi, L. & Yin, L. Quasi-Periodic Solutions for Non-Autonomous mKdV Equation. Indian J Pure Appl Math 49, 313–337 (2018). https://doi.org/10.1007/s13226-018-0271-x

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  • DOI: https://doi.org/10.1007/s13226-018-0271-x

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