Quasi-Periodic Solutions for Non-Autonomous mKdV Equation

Wenyan Cui, Lufang Mi () and Li Yin ()
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Wenyan Cui: Binzhou University
Lufang Mi: Binzhou University
Li Yin: Binzhou University

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 2, 313-337

Abstract: Abstract In this paper, we consider the non-autonomous modified Korteweg-de Vries (mKdV) equation $${u_t} = {u_{xxx}} - 6f\left( {\omega t} \right){u^2}{u_x},x \in \mathbb{R}/2\pi \mathbb{Z}$$ u t = u x x x − 6 f ( ω t ) u 2 u x , x ∈ ℝ / 2 π 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.

Keywords: Quasi-periodic solution; non-autonomous mKdV equation; KAM theory; normal form (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0271-x

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