A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

作者：Chvartatskyi O I^*; Sydorenko Yu M

来源：Journal of Mathematical Physics, 2013, 54(11): 113508.

DOI：10.1063/1.4830025

We introduce a new bidirectional generalization of (2+ 1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+ 1)-BDk-cKPH). This new hierarchy generalizes (2+ 1)-dimensional k-cKP hierarchy, (tA, tau B) and (gamma(A), sigma(B)) matrix hierarchies. (2+ 1)-BDk-cKPH contains a new matrix (1+ 1)-k-constrained KP hierarchy. Some members of (2+ 1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of Davey-Stewartson (DS) systems, (2+ 1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+ 1)-BDk-cKPH also includes new matrix (2+ 1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+ 1)-BDk-cKPH. As an example the exact form of multi-soliton solutions for vector generalization of the DS system is given.

• 出版日期2013-11