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Research PapersNo Access

VARIABLE-COEFFICIENT MIURA TRANSFORMATIONS AND INTEGRABLE PROPERTIES FOR A GENERALIZED VARIABLE-COEFFICIENT KORTEWEG–de VRIES EQUATION FROM BOSE–EINSTEIN CONDENSATES WITH SYMBOLIC COMPUTATION

School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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Meteorology Center of Air Force Command Post, Changchun 130051, China

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School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China

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https://doi.org/10.1142/S0217979209049851Cited by:7 (Source: Crossref)

Abstract

In this paper, a generalized variable-coefficient Korteweg–de Vries (KdV) equation with the dissipative and/or perturbed/external-force terms is investigated, which arises in arterial mechanics, blood vessels, Bose gases of impenetrable bosons and trapped Bose–Einstein condensates. With the computerized symbolic computation, two variable-coefficient Miura transformations are constructed from such a model to the modified KdV equation under the corresponding constraints on the coefficient functions. Meanwhile, through these two transformations, a couple of auto-Bäcklund transformations, nonlinear superposition formulas and Lax pairs are obtained with the relevant constraints. Furthermore, the one- and two-solitonic solutions of this equation are explicitly presented and the physical properties and possible applications in some fields of these solitonic structures are discussed and pointed out.

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Vol. 23, No. 04

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Received 13 December 2007

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