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Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass

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Abstract

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed \(L^2\)-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger–Korteweg-de Vries systems.

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Acknowledgements

The authors are thankful to Professor John Albert and Professor Felipe Linares for their teaching. A. J. Corcho was partially supported by CAPES and CNPq/Edital Universal - 481715/2012-6, Brazil and M. Panthee acknowledges supports from Brazilian agencies: FAPESP 2016/25864-6 and CNPq 305483/2014-5.

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Authors and Affiliations

  1. Trocaire College, 360 Choate Ave, Buffalo, NY, 14220, USA

    Santosh Bhattarai

  2. Instituto de Matemática - Universidade Federal do Rio de Janeiro/UFRJ, Rio de Janeiro, RJ, Brazil

    Adán J. Corcho

  3. IMECC - UNICAMP, Campinas, SP, 13083-859, Brazil

    Mahendra Panthee

Authors
  1. Santosh Bhattarai
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  2. Adán J. Corcho
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  3. Mahendra Panthee
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Correspondence to Mahendra Panthee.

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Bhattarai, S., Corcho, A.J. & Panthee, M. Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass. J Dyn Diff Equat 30, 845–881 (2018). https://doi.org/10.1007/s10884-018-9660-4

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  • DOI: https://doi.org/10.1007/s10884-018-9660-4

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