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Dissipative periodic waves, solitons, and breathers of the nonlinear Schrödinger equation with complex potentials

F. Kh. Abdullaev1,2, V. V. Konotop1,3, M. Salerno4, and A. V. Yulin1

  • 1Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal
  • 2Physical-Technical Institute, Uzbek Academy of Sciences, 2-b G. Mavlyanov Str., 100084 Tashkent, Uzbekistan
  • 3Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Ed. C8, Piso 6, Lisboa 1749-016, Portugal
  • 4Dipartimento di Fisica “E.R. Caianiello,” CNISM and INFN-Gruppo Collegato di Salerno, Università di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy

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Phys. Rev. E 82, 056606 – Published 12 November, 2010

DOI: https://doi.org/10.1103/PhysRevE.82.056606

Abstract

Exact solutions for the generalized nonlinear Schrödinger equation with inhomogeneous complex linear and nonlinear potentials are found. We have found localized and periodic solutions for a wide class of localized and periodic modulations in the space of complex potentials and nonlinearity coefficients. Examples of stable and unstable solutions are given. We also demonstrated numerically the existence of stable dissipative breathers in the presence of an additional parabolic trap.

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References (13)

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Phys. Rev. E 82, 056606– Published 12 November, 2010
  • Received 10 March 2010

© 2010 American Physical Society

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