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Quasi-Periodic Solutions with Prescribed Frequency in Reversible Systems

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Abstract

In this paper, we obtain a family of small-amplitude real analytic quasi-periodic solutions for a class of derivative nonlinear Schrödinger equations, subject to Dirichlet boundary conditions, which correspond to infinite-dimensional reversible systems with critical unbounded perturbations. We prove that the frequencies of the quasi-periodic solutions, accordingly, the tangential frequencies of the invariant tori for these reversible systems can be in a fixed direction.

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Acknowledgments

The author is grateful to Jiansheng Geng and Jian Wu for their invaluable discussions. The author also thanks the anonymous referees for useful comments on the paper. The author is supported by NSFC Grant 11126100 and the Youth Sci-Tech Innovation Fund, NAU Grant KJ2010025. The author is also partially supported by Program for New Century Excellent Talents in University.

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  1. Department of Mathematics, Nanjing Agricultural University, 210095 , Nanjing, People’s Republic of China

    Xiufang Ren

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  1. Xiufang Ren
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Ren, X. Quasi-Periodic Solutions with Prescribed Frequency in Reversible Systems. J Dyn Diff Equat 26, 493–515 (2014). https://doi.org/10.1007/s10884-014-9383-0

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  • DOI: https://doi.org/10.1007/s10884-014-9383-0

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