Authors

K. Mallory;R. A. Van Gorder

Comments

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Abbreviated Journal Title

Phys. Rev. E

Keywords

GROSS-PITAEVSKII EQUATION; OPTICAL LATTICES; COLD ATOMS; WELL; DYNAMICS; SUPERFLUID; STATES; WAVE; SYSTEMS; Physics, Fluids & Plasmas; Physics, Mathematical

Abstract

Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation (NLS) modeling attractive Bose-Einstein condensates (BECs) in a small potential are obtained via a form of nonlinear perturbation. The focus here is on perturbations to the bright soliton solutions due to small potentials which either confine or repel the BECs: under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of the bright solitons. Importantly, we do not need to assume that the nonlinearity is small, as we perform a sort of nonlinear perturbation by allowing the zeroth-order perturbation term to be governed by a nonlinear equation. This is useful, in that it allows us to consider perturbations of bright solitons of arbitrary size. In some cases, exact solutions can be recovered, and these agree with known results from the literature. Several special cases are considered which involve confining potentials of specific relevance to BECs. We make several observations on the influence of the small potentials on the behavior of the perturbed bright solitons. The results demonstrate the difference between perturbed bright solitons in the attractive NLS and those results found in the repulsive NLS for dark solitons, as discussed by Mallory and Van Gorder, [Phys. Rev. E 88, 013205 (2013)]. Extension of these results to more spatial dimensions is mentioned.

Journal Title

Physical Review E

Volume

89

Issue/Number

1

Publication Date

1-1-2014

Document Type

Article

Language

English

First Page

11

WOS Identifier

WOS:000332167800006

ISSN

1539-3755

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