Approach to first-order exact solutions of the Ablowitz-Ladik equation

Adrian Ankiewicz; Nail Akhmediev; Falk Lederer

doi:10.1103/PhysRevE.83.056602

Approach to first-order exact solutions of the Ablowitz-Ladik equation

Adrian Ankiewicz^*, Nail Akhmediev, Falk Lederer

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE).

Original language	English
Article number	056602
Journal	Physical Review E
Volume	83
Issue number	5
DOIs	https://doi.org/10.1103/PhysRevE.83.056602
Publication status	Published - 4 May 2011

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abstract = "We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schr{\"o}dinger equation (NLSE).",

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N2 - We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE).

AB - We derive exact solutions of the Ablowitz-Ladik (A-L) equation using a special ansatz that linearly relates the real and imaginary parts of the complex function. This ansatz allows us to derive a family of first-order solutions of the A-L equation with two independent parameters. This novel technique shows that every exact solution of the A-L equation has a direct analog among first-order solutions of the nonlinear Schrödinger equation (NLSE).

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Approach to first-order exact solutions of the Ablowitz-Ladik equation

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