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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0606036 (nlin)
[Submitted on 13 Jun 2006]

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

Authors:Jing Ping Wang
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Abstract: 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 ${\mathbb C}$ or a noncommutative associative algebra. We prove that these hierarchies are indeed quasi-local in the commutative case as conjectured by Mikhailov and Yamilov in 1998. We propose a ring extension based on the symbolic representation. As examples, we give noncommutative versions of KP, mKP and Boussinesq equations.
Comments: 17 pages
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0606036 [nlin.SI]
  (or arXiv:nlin/0606036v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0606036
Journal reference: Journal of Mathematical Physics 47(11), 113508, 2006
Related DOI: https://doi.org/10.1063/1.2375032

Submission history

From: Jing Ping Wang [view email]
[v1] Tue, 13 Jun 2006 15:10:36 UTC (21 KB)
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