PMID: 11308785Apr 20, 2001Paper

Stability of multiple pulses in discrete systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
T KapitulaB A Malomed

Abstract

The stability of multiple-pulse solutions to the discrete nonlinear Schrödinger equation is considered. A bound state of widely separated single pulses is rigorously shown to be unstable, unless the phase shift Delta phi between adjacent pulses satisfies Delta phi=pi. This instability is accounted for by positive real eigenvalues in the linearized system. The analysis leading to the instability result does not, however, determine the linear stability of those multiple pulses for which Delta phi=pi between adjacent pulses. A direct variational approach for a two-pulse predicts that it is linearly stable if Delta phi=pi, and if the separation between the individual pulses satisfies a certain condition. The variational approach can easily be generalized to study the stability of N pulses for any N>or=3. The analysis is supplemented with a detailed numerical stability analysis.

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Citations

Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G KevrekidisA Saxena
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D V Skryabin
Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G Kevrekidis
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hadi Susanto, Magnus Johansson
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hidetsugu Sakaguchi, Boris A Malomed
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Gomez-GardeñesA R Bishop
Dec 13, 2006·Physical Review Letters·Y LinzonS Bar-Ad
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hervé LeblondDumitru Mihalache
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K J H LawA R Bishop
May 30, 2015·Reports on Progress in Physics·Omjyoti DuttaJakub Zakrzewski
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G KevrekidisE S Titi
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C WangB A Malomed
Dec 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hidetsugu Sakaguchi, Yusuke Kageyama
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J HudockD N Christodoulides
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Panayotis G KevrekidisAlexander S Kovalev
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Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I V Barashenkov, E V Zemlyanaya
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Boris A MalomedRobert A Van Gorder
Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·B A Malomed, P G Kevrekidis
Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G KevrekidisB A Malomed
Aug 11, 2005·Physical Review Letters·R Carretero-GonzálezD J Frantzeskakis
Mar 23, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrey A Sukhorukov, Yuri S Kivshar

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