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Existence of Minimizers for Some Coupled Nonlinear Schrödinger Equations

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Geometric Properties for Parabolic and Elliptic PDE's

Part of the book series: Springer INdAM Series ((SINDAMS,volume 2))

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Abstract

The existence and nonexistence of minimizers for two minimizing problems are considered. These problems are related to three coupled nonlinear Schrödinger equations which appear in the field of nonlinear optics. We observe the relationship between two minimizing problems and also study the asymptotic behavior when the coefficient standing for the nonlocal nonlinearity tend to 0.

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Acknowledgements

The author would like to thank Professor Maris and Professor Shibata for letting him know Refs. [10] and [28], and fruitful discussions. The author was supported by Grant-in-Aid for JSPS Fellows 22-1561 and “Japanese-German Graduate Externship, International Research Training Group” associated with Waseda University and Technische Universität Darmstadt.

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Authors and Affiliations

  1. Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai-Shi, Miyagi, 980-8578, Japan

    Norihisa Ikoma

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  1. Norihisa Ikoma
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Correspondence to Norihisa Ikoma .

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Editors and Affiliations

  1. Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, Firenze, 50124, Italy

    Rolando Magnanini

  2. Graduate School of Information Sciences, Division of Mathematics, Tohoku University, Sendai, 980-8579, Japan

    Shigeru Sakaguchi

  3. , Dipartimento di Matematica ed Applicazio, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, Napoli, 80126, Italy

    Angelo Alvino

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Ikoma, N. (2013). Existence of Minimizers for Some Coupled Nonlinear Schrödinger Equations. In: Magnanini, R., Sakaguchi, S., Alvino, A. (eds) Geometric Properties for Parabolic and Elliptic PDE's. Springer INdAM Series, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2841-8_10

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