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Contemporary Mathematics Multi-Soliton Complexes
 

Summary: Contemporary Mathematics
Multi-Soliton Complexes
Nail N. Akhmediev, Andrey A. Sukhorukov, and Adrian Ankiewicz
Abstract. This paper reviews the latest advances in the area of multi-soliton
complexes(MSCs). We present exact analyticalsolutions of coupled nonlinear
Schrodingerequations,which describe multi-solitoncomplexesand their inter-
actions on top of a background in media with self-focusing or self-defocusing
Kerr-like nonlinearities. We present numerical examples illustrating the re-
markable properties of MSCs, such as their reshaping after collisions. This
occurs because the fundamental solitons composing an MSC can acquire dif-
ferent lateral shifts. We also obtain an accurate estimate for the peak intensi-
ties of stationaryand interactingMSCs, by establishinga rigorousrelationship
between the eigenvalues of incoherently{coupledfundamental solitons and the
range of admissible intensities.
1. Introduction
Dynamic nonlinear systems have properties which were initially surprising to
scientists FPU55, Fer65, A01]. The concept of`solitons', rst introduced in ZK65],
helped to demistify at least some of these surprises. The inverse scattering tech-
nique, developed later in a number of works GGKM67, ZS71, AKNS74], gave
scientists a powerful tool for understanding and for investigating the properties of

  

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