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From the Zakharov system to the NLS equation on the torus

  • Raphael Taraca and Guido Schneider EMAIL logo
Published/Copyright: July 9, 2025

Abstract

The NLS equation can be derived from the Zakharov system in a singular limit. The goal of this paper is to add some new aspects to the existing analysis about this approximation. We outline the differences between the situation x and x 𝕋 = / ( 2 π ) . We explain the difficulties occurring in the construction of higher order approximations and use these approximations to improve the approximation rate. Moreover, we point out that the standard validity proof requires a smallness condition which was not stated in the existing literature.

MSC 2020: 35A35; 35Q55

Funding statement: The paper is partially supported by the Deutsche Forschungsgemeinschaft DFG through the SFB 1173 “Wave phenomena” Project-ID 258734477.

Acknowledgements

The authors would like to thank the referees for many helpful comments.

References

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Received: 2024-10-26
Revised: 2025-06-20
Accepted: 2025-06-22
Published Online: 2025-07-09

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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