ASYMPTOTIC STABILITY OF SMALL BOUND STATES IN THE DISCRETE NONLINEAR SCHRODINGER EQUATION
Publication Date
2009
Journal or Book Title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
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.
Pages
2010-2030
Volume
41
Issue
5
Recommended Citation
Kevrekidis, PG; Pelinovsky, DE; and Stefanov, A, "ASYMPTOTIC STABILITY OF SMALL BOUND STATES IN THE DISCRETE NONLINEAR SCHRODINGER EQUATION" (2009). SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 23.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/23
Comments
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