Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 400, Issue 2, Pages 624-634Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.11.028
Keywords
Binary Bell polynomial; Lax pair; Darboux covariant Lax pair; Backlund transformation; Infinite conservation law; N-soliton solution
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Funding
- National Natural Science Foundation of China [11075055]
- Innovative Research Team Program of the National Natural Science Foundation of China [61021004]
- Shanghai Leading Academic Discipline Project [B412]
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This paper investigates the integrability of a generalized (2+1)-dimensional Korteweg-de Vries equation. With the aid of binary Bell polynomials, its bilinear formalism, bilinear Backlund transformation, Lax pair and Darboux covariant Lax pair are succinctly constructed, which can be reduced to the ones of several integrable equations such as the Korteweg-de Vries equation and the Calogero-Bogoyavlenskii-Schiff equation. Moreover, the infinite conservation laws of the generalized (2+1)-dimensional Korteweg-de Vries equation are found by virtue of binary Bell polynomials. All conserved densities and fluxes are given with explicit recursion formulas. (C) 2012 Elsevier Inc. All rights reserved.
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