Moving solitons in the damped Ablowitz-Ladik model driven by a standing wave

David Cai; A. R. Bishop; Niels Grønbech-Jensen; Boris A. Malomed

doi:10.1103/PhysRevE.50.R694

Moving solitons in the damped Ablowitz-Ladik model driven by a standing wave

David Cai, A. R. Bishop, Niels Grønbech-Jensen, Boris A. Malomed

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We predict theoretically that, via a resonance mechanism, stable moving solitons exist in a discrete (1+1)-dimensional nonlinear Schrödinger (Ablowitz-Ladik) equation with dissipation and an ac driving term in the form of a standing wave. Agreement between the predicted threshold (minimum) values of the strength of the drive which is able to sustain the moving solitons and those measured in direct numerical simulations is excellent. Our results show an example of multistability in damped, standing-wave-driven systems. The dynamical instability for the motion of solitons in the unstable regimes is also analyzed.

Original language	English (US)
Pages (from-to)	R694-R697
Journal	Physical Review E
Volume	50
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.50.R694
State	Published - 1994

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Condensed Matter Physics

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10.1103/PhysRevE.50.R694

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abstract = "We predict theoretically that, via a resonance mechanism, stable moving solitons exist in a discrete (1+1)-dimensional nonlinear Schr{\"o}dinger (Ablowitz-Ladik) equation with dissipation and an ac driving term in the form of a standing wave. Agreement between the predicted threshold (minimum) values of the strength of the drive which is able to sustain the moving solitons and those measured in direct numerical simulations is excellent. Our results show an example of multistability in damped, standing-wave-driven systems. The dynamical instability for the motion of solitons in the unstable regimes is also analyzed.",

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AB - We predict theoretically that, via a resonance mechanism, stable moving solitons exist in a discrete (1+1)-dimensional nonlinear Schrödinger (Ablowitz-Ladik) equation with dissipation and an ac driving term in the form of a standing wave. Agreement between the predicted threshold (minimum) values of the strength of the drive which is able to sustain the moving solitons and those measured in direct numerical simulations is excellent. Our results show an example of multistability in damped, standing-wave-driven systems. The dynamical instability for the motion of solitons in the unstable regimes is also analyzed.

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Moving solitons in the damped Ablowitz-Ladik model driven by a standing wave

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