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

Adrian Ankiewicz | Zendy; Nail Akhmediev | Zendy; F. Lederer | Zendy

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

Author(s) -

Adrian Ankiewicz,

Nail Akhmediev,

F. Lederer

Publication year - 2011

Publication title -

physical review e

Language(s) - English

Resource type - Journals

eISSN - 1550-2376

pISSN - 1539-3755

DOI - 10.1103/physreve.83.056602

Subject(s) - ansatz , exact solutions in general relativity , order (exchange) , mathematics , function (biology) , nonlinear system , nonlinear schrödinger equation , mathematical analysis , mathematical physics , physics , schrödinger equation , quantum mechanics , finance , evolutionary biology , economics , biology

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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