Dissipative periodic waves, solitons, and breathers of the nonlinear Schr\"odinger equation with complex potentials

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

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin

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

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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Received 10 March 2010

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

Authors & Affiliations

F. Kh. Abdullaev^1,2, V. V. Konotop^1,3, 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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Vol. 82, Iss. 5 — November 2010

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

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

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin

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

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

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

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin

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

Abstract

Authors & Affiliations

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