In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti–Leon–Manna–Pempinelli model, and (2+1)-dimensional Sawada–Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Bäcklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Bäcklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Bäcklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Bäcklund transformations can be linearized into the corresponding Lax pairs.
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November 2010
Research Article|
November 24 2010
Bell-polynomial manipulations on the Bäcklund transformations and Lax pairs for some soliton equations with one Tau-function
Xing Lü;
Xing Lü
1School of Science,
Beijing University of Posts and Telecommunications
, P.O. Box 122, Beijing 100876, China
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Bo Tian;
Bo Tian
a)
1School of Science,
Beijing University of Posts and Telecommunications
, P.O. Box 122, Beijing 100876, China
2State Key Laboratory of Software Development Environment,
Beijing University of Aeronautics and Astronautics
, Beijing 100191, China
3Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education,
Beijing University of Posts and Telecommunications
, P.O. Box 128, Beijing 100876, China
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Kun Sun;
Kun Sun
1School of Science,
Beijing University of Posts and Telecommunications
, P.O. Box 122, Beijing 100876, China
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Pan Wang
Pan Wang
1School of Science,
Beijing University of Posts and Telecommunications
, P.O. Box 122, Beijing 100876, China
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a)
Electronic mail: tian.bupt@yahoo.com.cn.
J. Math. Phys. 51, 113506 (2010)
Article history
Received:
August 14 2010
Accepted:
September 28 2010
Citation
Xing Lü, Bo Tian, Kun Sun, Pan Wang; Bell-polynomial manipulations on the Bäcklund transformations and Lax pairs for some soliton equations with one Tau-function. J. Math. Phys. 1 November 2010; 51 (11): 113506. https://doi.org/10.1063/1.3504168
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