Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation

Chaos
Sergey V Dmitriev, Takeshi Shigenari

Abstract

Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.

References

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Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S V DmitrievT Shigenari
Oct 1, 1993·Chaos·Edward Ott, Tamas Tel

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Citations

Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I E PapacharalampousD J Frantzeskakis
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergey V DmitrievTakeshi Shigenari
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S V DmitrievD J Frantzeskakis
Jun 4, 2008·Physical Review Letters·Yi ZhuJianke Yang
Feb 3, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yusuke Doi
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bin LiuShu-Jing Li
May 21, 2005·Physical Review Letters·V Ahufinger, A Sanpera
Nov 13, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergey V DmitrievYuri S Kivshar
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yi Zhu, Jianke Yang

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