Perturbation-induced radiation by the Ablowitz-Ladik soliton

Abstract

An efficient formalism is elaborated to analytically describe dynamics of the Ablowitz-Ladik soliton in the presence of perturbations. This formalism is based on using the Riemann-Hilbert problem and provides the means of calculating evolution of the discrete soliton parameters, as well as shape distortion and perturbation-induced radiation effects. As an example, soliton characteristics are calculated for linear damping and quintic perturbations.

arXiv comment13 pages, 4 figures, Phys. Rev. E (in press)

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• Nonlocal reductions of the Ablowitz-Ladik equation
• Solitons in strongly driven discrete nonlinear Schrödinger-type models
• Dynamics of subpicosecond dispersion-managed soliton in a fibre: A perturbative analysis
• The discrete mKdV equation revisited: a Riemann-Hilbert approach