Exact solitary- and periodic-wave modes in coupled equations with saturable nonlinearity

K. W. Chow, B. A. Malomed, Nakkeeran Kaliyaperumal

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We demonstrate that the known method, based on the Hirota bilinear operator, generates classes of exact solutions to a system of coupled nonlinear Schrodinger (CNLS) equations with nonpolynomial nonlinearity, either rational or algebraic (the latter involves a square root). The choice of the CNLS equations is suggested by known models for photorefractive media and Bose-Einstein condensation: The solutions are, generally, periodic, and they form families expressed in terms of the Jacobi elliptic functions, the elliptic modulus k being a free parameter of the family. In the limit case corresponding to the infinite period (k=1), the solutions amount to solitons. In some cases, the exact solutions may feature patterns with two peaks per period. Exact solutions are also found in a single NLS equation with a rational saturable nonlinearity and periodic potential in the form of squared Jacobi sine. (c) 2006 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)37-41
Number of pages4
JournalPhysics Letters A
Volume359
DOIs
Publication statusPublished - 2006

Keywords

  • SCHRODINGER-EQUATIONS
  • VECTOR SOLITONS
  • SPATIAL SOLITONS
  • OPTICAL-FIBER
  • INSTABILITIES
  • SYSTEM

Cite this

Exact solitary- and periodic-wave modes in coupled equations with saturable nonlinearity. / Chow, K. W.; Malomed, B. A.; Kaliyaperumal, Nakkeeran.

In: Physics Letters A, Vol. 359, 2006, p. 37-41.

Research output: Contribution to journalArticle

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AU - Kaliyaperumal, Nakkeeran

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N2 - We demonstrate that the known method, based on the Hirota bilinear operator, generates classes of exact solutions to a system of coupled nonlinear Schrodinger (CNLS) equations with nonpolynomial nonlinearity, either rational or algebraic (the latter involves a square root). The choice of the CNLS equations is suggested by known models for photorefractive media and Bose-Einstein condensation: The solutions are, generally, periodic, and they form families expressed in terms of the Jacobi elliptic functions, the elliptic modulus k being a free parameter of the family. In the limit case corresponding to the infinite period (k=1), the solutions amount to solitons. In some cases, the exact solutions may feature patterns with two peaks per period. Exact solutions are also found in a single NLS equation with a rational saturable nonlinearity and periodic potential in the form of squared Jacobi sine. (c) 2006 Elsevier B.V. All rights reserved.

AB - We demonstrate that the known method, based on the Hirota bilinear operator, generates classes of exact solutions to a system of coupled nonlinear Schrodinger (CNLS) equations with nonpolynomial nonlinearity, either rational or algebraic (the latter involves a square root). The choice of the CNLS equations is suggested by known models for photorefractive media and Bose-Einstein condensation: The solutions are, generally, periodic, and they form families expressed in terms of the Jacobi elliptic functions, the elliptic modulus k being a free parameter of the family. In the limit case corresponding to the infinite period (k=1), the solutions amount to solitons. In some cases, the exact solutions may feature patterns with two peaks per period. Exact solutions are also found in a single NLS equation with a rational saturable nonlinearity and periodic potential in the form of squared Jacobi sine. (c) 2006 Elsevier B.V. All rights reserved.

KW - SCHRODINGER-EQUATIONS

KW - VECTOR SOLITONS

KW - SPATIAL SOLITONS

KW - OPTICAL-FIBER

KW - INSTABILITIES

KW - SYSTEM

U2 - 10.1016/j.physleta.2006.05.082

DO - 10.1016/j.physleta.2006.05.082

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