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The cauchy problem for coupled nonlinear Schrödinger equations with linear damping: Local and global existence and blowup of solutions

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Abstract

The authors study, by applying and extending the methods developed by Cazenave (2003), Dias and Figueira (2014), Dias et al. (2014), Glassey (1994–1997), Kato (1987), Ohta and Todorova (2009) and Tsutsumi (1984), the Cauchy problem for a damped coupled system of nonlinear Schrödinger equations and they obtain new results on the local and global existence of H 1-strong solutions and on their possible blowup in the supercritical case and in a special situation, in the critical or supercritical cases.

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Authors and Affiliations

  1. CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    João-Paulo Dias & Mário Figueira

  2. Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed.C8, 1749-016, Lisboa, Portugal

    Vladimir V. Konotop

Authors
  1. João-Paulo Dias
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  2. Mário Figueira
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  3. Vladimir V. Konotop
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Corresponding author

Correspondence to João-Paulo Dias.

Additional information

This work was supported by the Fundação para a Ciência e Tecnologia (Portugal) (Nos. PEst-OE/MAT/UI0209/2013, UID/MAT/04561/2013, PTDC/FIS-OPT/1918/2012, UID/FIS/00618/2013).

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Dias, JP., Figueira, M. & Konotop, V.V. The cauchy problem for coupled nonlinear Schrödinger equations with linear damping: Local and global existence and blowup of solutions. Chin. Ann. Math. Ser. B 37, 665–682 (2016). https://doi.org/10.1007/s11401-016-1006-0

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  • DOI: https://doi.org/10.1007/s11401-016-1006-0

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