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Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials

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Abstract

In this paper, we show the existence of a minimizer for the \(L^2\)-constrained minimization problem associated with a nonlinear Schrödinger system with three wave interaction without assuming symmetry for potentials.

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Acknowledgements

The author would like to thank the referees for carefully reading my manuscript and for giving many useful comments. The author would like to thank Professor N. Ikoma sending us their paper [10] and [11] and for telling us about the applicability of their method to the nonlinear Schrödinger system with three wave interaction. The author apologize that the author should refer [11] instead of [10] in [12] and that in completing the paper [12] the author did not realize exponential decay properties of solutions to our system and gave a misleading comment on [10].

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tokyo Metropolitan University, 1-1 Minami, Osawa, Hachioji, Tokyo, 192-0397, Japan

    Yuki Osada

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  1. Yuki Osada
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Correspondence to Yuki Osada.

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This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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Osada, Y. Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials. Partial Differ. Equ. Appl. 3, 28 (2022). https://doi.org/10.1007/s42985-022-00160-9

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  • DOI: https://doi.org/10.1007/s42985-022-00160-9

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