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On the structure of (2+1)-dimensional commutative and noncommutative integrable equations

Wang, Jing Ping (2006) On the structure of (2+1)-dimensional commutative and noncommutative integrable equations. Journal of Mathematical Physics, 47 (11). p. 113508. ISSN 0022-2488. (doi:10.1063/1.2375032) (KAR id:3370)


We develop the symbolic representation method to derive the hierarchies of (2+1)-dimensional integrable equations from the scalar Lax operators and to study their properties globally. The method applies to both commutative and noncommutative cases in the sense that the dependent variable takes its values in C or a noncommutative associative algebra. We prove that these hierarchies are indeed quasi-local in the commutative case as conjectured by Mikhailov and Yamilov [J. Phys. A 31, 6707 (1998)]. We propose a ring extension in the noncommutative case based on the symbolic representation. As examples, we give noncommutative versions of Kadomtsev-Petviashvili (KP), modified Kadomtsev-Petviashvili (mKP), and Boussinesq equations.

Item Type: Article
DOI/Identification number: 10.1063/1.2375032
Subjects: Q Science
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Jing Ping Wang
Date Deposited: 29 Aug 2008 15:31 UTC
Last Modified: 16 Nov 2021 09:41 UTC
Resource URI: (The current URI for this page, for reference purposes)

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