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

Article, Preprint English OPEN
Wang, Jing Ping (2006)
  • Publisher: American Institute of Physics
  • Related identifiers: doi: 10.1063/1.2375032
  • Subject: Q | Nonlinear Sciences - Exactly Solvable and Integrable Systems
    arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems

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.
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