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Asymptotic stability of small solitons in the discrete nonlinear Schrödinger equation in one dimension
Kevrekidis, P. G. Pelinovsky, Dmitry E. Stefanov, Atanas G.
Kevrekidis, P. G.
Pelinovsky, Dmitry E.
Stefanov, Atanas G.
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Abstract
Asymptotic stability of small bound states in one dimension is proved in the framework of a discrete nonlinear Schrödinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dispersive decay estimates from Pelinovsky and Stefanov [J. Math. Phys., 49 (2008), 113501] and the arguments of Mizumachi [J. Math. Kyoto Univ., 48 (2008), pp. 471–497] for a continuous nonlinear Schrödinger equation in one dimension. Numerical simulations suggest that the actual decay rate of perturbations near the asymptotically stable bound states is higher than the one used in the analysis.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/080737654.
Date
2009-11-05
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Society for Industrial and Applied Mathematics
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Keywords
discrete nonlinear Schrodinger equations, bound states, asymptotic stability, Strichartz estimates
Citation
P. G. Kevrekidis, D. E. Pelinovsky, and A. Stefanov. "Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation." (2009) SIAM J. Math. Anal., 41(5), 2010–2030. (21 pages). http://dx.doi.org/10.1137/080737654.