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Birkhoff Normal Form for the Derivative Nonlinear Schrödinger Equation

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Abstract

This paper is concerned with the derivative nonlinear Schrödinger equation with periodic boundary conditions. We obtain complete Birkhoff normal form of order six. As an application, the long time stability for solutions of small amplitude is proved.

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Acknowledgements

The author is grateful to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610065, P. R. China

    Jian Jun Liu

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  1. Jian Jun Liu
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Correspondence to Jian Jun Liu.

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Supported by NNSFC (Grant Nos. 11671280, 11822108) and Fok Ying Tong Education Foundation (Grant No. 161002)

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Liu, J.J. Birkhoff Normal Form for the Derivative Nonlinear Schrödinger Equation. Acta. Math. Sin.-English Ser. 38, 249–262 (2022). https://doi.org/10.1007/s10114-022-0472-4

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  • DOI: https://doi.org/10.1007/s10114-022-0472-4

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