Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation | Zendy

P. G. Kevrekidis | Zendy; Dmitry E. Pelinovsky | Zendy; Atanas Stefanov | Zendy

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Asymptotic Stability of Small Bound States in the Discrete Nonlinear Schrödinger Equation

Author(s) -

P. G. Kevrekidis,

Dmitry E. Pelinovsky,

Atanas Stefanov

Publication year - 2009

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/080737654

Subject(s) - mathematics , eigenvalues and eigenvectors , dimension (graph theory) , nonlinear system , mathematical analysis , bound state , exponential stability , upper and lower bounds , nonlinear schrödinger equation , schrödinger equation , stability (learning theory) , simple (philosophy) , mathematical physics , quantum mechanics , pure mathematics , physics , philosophy , epistemology , machine learning , computer science

Asymptotic stability of small bound states in one dimension is proved in the frame- work of a discrete nonlinear Schrodinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dis- persive 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 Schrodinger 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.

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