Internal modes of discrete solitons near the anti-continuum limit of the dNLS equation

PHYSICA D-NONLINEAR PHENOMENA

卷:240

Article

Pelinovsky, Dmitry¹  Sakovich, Anton¹ 

[1] McMaster Univ, Dept Math, Hamilton, ON L8S 4K1, Canada

关键词: Discrete NLS equation;    Anti-continuum limit;    Internal modes;    Resolvent operator;   

DOI  :  10.1016/j.physd.2010.09.002

来源: Elsevier

【 摘 要 】

Discrete solitons of the discrete nonlinear Schrodinger (dNLS) equation are compactly supported in the anti-continuum limit of the zero coupling between lattice sites. Eigenvalues of the linearization of the dNLS equation at the discrete soliton determine its spectral stability. Small eigenvalues bifurcating from the zero eigenvalue near the anti-continuum limit were characterized earlier for this model. Here we analyze the resolvent operator and prove that it is bounded in the neighborhood of the continuous spectrum if the discrete soliton is simply connected in the anti-continuum limit. This result rules out the existence of internal modes (neutrally stable eigenvalues of the discrete spectrum) near the anti-continuum limit. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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