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PHYSICAL REVIEW E 83, 056602 (2011) Approach to first-order exact solutions of the Ablowitz-Ladik equation
 

Summary: PHYSICAL REVIEW E 83, 056602 (2011)
Approach to first-order exact solutions of the Ablowitz-Ladik equation
Adrian Ankiewicz,1
Nail Akhmediev,1
and Falk Lederer2
1
Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies,
The Australian National University, Canberra ACT 0200, Australia
2
Institute of Condensed Matter Theory and Solid State Optics, Friedrich-Schiller-Universit¨at Jena,
Max-Wien-Platz 1, D-07743 Jena, Germany
(Received 24 December 2010; published 4 May 2011)
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¨odinger equation (NLSE).
DOI: 10.1103/PhysRevE.83.056602 PACS number(s): 05.45.Yv, 45.05.+x, 42.81.Qb, 42.65.Wi
I. INTRODUCTION
Extreme waves, for example, optical needles, can occur
in spatially extended systems. Recently, such waves have

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics