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On the Existence of Dark Solitons in a Cubic-Quintic Nonlinear Schrödinger Equation with a Periodic Potential

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Abstract

A proof of the existence of stationary dark soliton solutions of a cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic of the Poincaré map.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Granada, 18071, Granada, Spain

    Pedro J. Torres

  2. Centro de Física Teórica e Computacional, Universidade de Lisboa, Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, Lisbon, 1649-003, Portugal

    Vladimir V. Konotop

  3. Departamento de Física, Universidade de Lisboa, Campo Grande, Ed. C8, Piso 6, Lisboa, 1749-016, Portugal

    Vladimir V. Konotop

Authors
  1. Pedro J. Torres
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  2. Vladimir V. Konotop
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Corresponding author

Correspondence to Pedro J. Torres.

Additional information

Communicated by P. Constantin

The work of PJT was supported by D.G.I. MTM2005-03483, Ministerio de Educación y Ciencia, Spain.

The work of VVK was supported by the Secretaria de Estado de Universidades e Investigación (Spain) under the grant SAB2005-0195 and by the FCT (Portugal) and European program FEDER under the grant POCI/FIS/56237/2004.

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Torres, P.J., Konotop, V.V. On the Existence of Dark Solitons in a Cubic-Quintic Nonlinear Schrödinger Equation with a Periodic Potential. Commun. Math. Phys. 282, 1–9 (2008). https://doi.org/10.1007/s00220-008-0527-0

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  • DOI: https://doi.org/10.1007/s00220-008-0527-0

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