Bell-polynomial manipulations on the Baecklund transformations and Lax pairs for some soliton equations with one Tau-function

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3504168· OSTI ID:21501206

Xing, Lue; Kun, Sun; Pan, Wang ^[1]; Bo, Tian ^[1]

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

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 Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the corresponding Lax pairs.

• OSTI ID: 21501206
• Journal Information: Journal of Mathematical Physics, Vol. 51, Issue 11; Other Information: DOI: 10.1063/1.3504168; (c) 2010 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
BAECKLUND TRANSFORMATION
BELL THEOREM
CALCULATION METHODS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
SCALE INVARIANCE
SOLITONS
WATER WAVES
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
GRAVITY WAVES
INVARIANCE PRINCIPLES
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
TRANSFORMATIONS