Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Non-Vanishing Continuous Background

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dc.creatorKitaev, A. V.
dc.creatorVartanian, A. H.
dc.date1997-12-27
dc.date.accessioned2026-07-07T06:17:29Z
dc.date.available2026-07-07T06:17:29Z
dc.descriptionUsing the matrix Riemann-Hilbert factorization approach for nonlinear evolution systems which take the form of Lax-pair isospectral deformations and whose corresponding Lax operators contain both discrete and continuous spectra, the leading-order asymptotics as $t \to \pm \infty$ of the solution to the Cauchy problem for the modified nonlinear Schrödinger equation, $i \partial_{t} u + {1/2} \partial_{x}^{2} u + | u |^{2} u + i s \partial_{x} (| u |^{2} u) = 0$, $s \in \Bbb R_{>0}$, which is a model for nonlinear pulse propagation in optical fibers in the subpicosecond time scale, are obtained: also derived are analogous results for two gauge-equivalent nonlinear evolution equations; in particular, the derivative nonlinear Schrödinger equation, $i \partial_{t} q + \partial_{x}^{2} q - i \partial_{x} (| q |^{2} q) = 0$. As an application of these asymptotic results, explicit expressions for position and phase shifts of solitons in the presence of the continuous spectrum are calculated.
dc.description38 pages, 1 figure, LaTeX
dc.identifierhttps://arxiv.org/abs/solv-int/9801001
dc.identifierhttp://arxiv.org/abs/solv-int/9801001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94404
dc.subjectExactly Solvable and Integrable Systems
dc.titleAsymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Non-Vanishing Continuous Background
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