Noncommutative KP Hierarchy and Hirota Triple-Product Relations

• Wang Ning

  Department of Physics, Ocean University of China

• Wadati Miki

  Department of Physics, Graduate School of Science, University of Tokyo

Abstract

We study τ-function representation of solutions and deformation of Hirota bilinear relations for a noncommutative Kadomtsev–Petviashvili (NC KP) hierarchy. An operator-valued τ-function representation of solutions for the NC KP hierarchy is presented. In contrast to the commutative case, the admissible τ-function satisfies an additional triangle-like relation. Furthermore, instead of the commutative Hirota bilinear relations, a set of triple-product relations such as Hirota triple-product differential/difference equations is found. Noncommutative deformation of multi-line soliton solutions of the NC KP hierarchy is also investigated. It is shown that for an arbitrary noncommutative parameter, the corresponding operator-valued τ-function in general is expressed in the form of infinite series.

Journal

• Journal of the Physical Society of Japan

  Journal of the Physical Society of Japan 73 (7), 1689-1698, 2004

  THE PHYSICAL SOCIETY OF JAPAN

Keywords

• noncommutative KP hierarchy
• triangle-like relation
• operator-valued “τ-function”
• Hirota triple-product relations
• multi-line soliton solutions

Details

• CRID: 1390001204186623488
• NII Article ID: 210000104892
• NII Article ID: 110001954880
• NII Book ID: AA00704814
• DOI: 10.1143/jpsj.73.1689
• BIBCODE: 2004JPSJ...73.1689W
• ISSN: 13474073
• ISSN: 00319015
• MRID: 2095463
• NDL BIB ID: 7004106
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7004106
• Web Site: http://journals.jps.jp/doi/pdf/10.1143/JPSJ.73.1689
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed