Springer LINK: The European Physical Journal B - Abstract Volume 3 Issue 1 (1998) pp 23-33

The European Physical Journal B

ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)

Table of Contents

Abstract Volume 3 Issue 1 (1998) pp 23-33

The role of power law nonlinearity in the discrete nonlinear Schrödinger equation on the formation of stationary localized states in the Cayley tree

K. Kundu (a), B.C. Gupta

Institute of physics, Sachivalaya Marg, Bhubaneswar 751005, India

Received: 18 September 1997 / Revised: 31 October and 17 november 1997 / Accepted: 19 November 1997

Abstract: We study the formation of stationary localized states using the discrete nonlinear Schrödinger equation in a Cayley tree with connectivity K. Two cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear system are considered. We introduce a transformation which reduces the Cayley tree into an one dimensional chain with a bond defect. The hopping matrix element between the impurity sites is reduced by $1/\sqrt K$. The transformed system is also shown to yield tight binding Green's function of the Cayley tree. The dimeric ansatz is used to find the reduced Hamiltonian of the system. Stationary localized states are found from the fixed point equations of the Hamiltonian of the reduced dynamical system. We discuss the existence of different kinds of localized states. We have also analyzed the formation of localized states in one dimensional system with a bond defect and nonlinearity which does not correspond to a Cayley tree. Stability of the states is discussed and stability diagram is presented for few cases. In all cases the total phase diagram for localized states have been presented.

PACS. 71.55.-i Impurity and defect levels[:AND:] 72.10.Fk Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect)

(a) email: kundu@Breathers.iopb.stpbh.soft.net

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