Appearance of bound states in random potentials with applications to soliton theory

Derevyanko, Stanislav (2011). Appearance of bound states in random potentials with applications to soliton theory. Physical Review E, 84 (1),


We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

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Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Electrical, electronic & power engineering
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: stochastic creation,single bound state ,random potential,compact support,Hermitian Schrödinger equation,non-Hermitian Zakharov-Shabat systems,inverse scattering method,Korteveg–de-Vries,nonlinear Schrödinger equations,eigenvalue creation,Statistics and Probability,Condensed Matter Physics,Statistical and Nonlinear Physics
Full Text Link: http://link.aps ... sRevE.84.016601
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2011-07-06
Authors: Derevyanko, Stanislav



Version: Published Version

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