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Research PapersNo Access

MODULATIONAL INSTABILITY AND EXACT SOLITON AND PERIODIC SOLUTIONS FOR TWO WEAKLY COUPLED EFFECTIVELY 1D CONDENSATES TRAPPED IN A DOUBLE-WELL POTENTIAL

Department of Mathematics and Computer Sciences, Faculty of Science, University of Dschang, P.O. Box 4509, Douala, Republic of Cameroon

Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada

Corresponding author.

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,

R. VAILLANCOURT

Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave, Ottawa, ON K1N 6N5, Canada

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, and

Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel

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https://doi.org/10.1142/S021797921005541XCited by:6 (Source: Crossref)

Abstract

The modulational instability of the coupled Gross–Pitaevskii equation (alias nonlinear Schrödinger equation), which describes two Bose–Einstein condensates trapped in an asymmetric double-well potential, is investigated. The nonlinear dispersion relation that relates the frequency and wave number of the modulating perturbations is found and its analysis shows several possibilities for the modulational stability region. Exact soliton and periodic solutions are constructed via elliptic ordinary differential equations.

Keywords:

PACS: 03.75.Gg, 03.75.Nt, 03.75.Hh, 02.60.Cb

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Vol. 24, No. 14

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Received 22 December 2008

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