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

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 techniqu...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 83; no. 5 Pt 2; p. 056602
Main Authors Ankiewicz, Adrian, Akhmediev, Nail, Lederer, Falk
Format Journal Article
LanguageEnglish
Published United States 04.05.2011
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Summary: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).
ISSN:1550-2376
DOI:10.1103/physreve.83.056602