A new bidirectional generalization of (2+1)dimensional matrix kconstrained KadomtsevPetviashvili hierarchy
Abstract
We introduce a new bidirectional generalization of (2+1)dimensional kconstrained KadomtsevPetviashvili (KP) hierarchy ((2+1)BDkcKPH). This new hierarchy generalizes (2+1)dimensional kcKP hierarchy, (t_{A}, τ_{B}) and (γ_{A}, σ_{B}) matrix hierarchies. (2+1)BDkcKPH contains a new matrix (1+1)kconstrained KP hierarchy. Some members of (2+1)BDkcKPH are also listed. In particular, it contains matrix generalizations of DaveyStewartson (DS) systems, (2+1)dimensional modified Kortewegde Vries equation and the Nizhnik equation. (2+1)BDkcKPH also includes new matrix (2+1)dimensional generalizations of the YajimaOikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)BDkcKPH. As an example the exact form of multisoliton solutions for vector generalization of the DS system is given.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 2013
 DOI:
 10.1063/1.4830025
 arXiv:
 arXiv:1303.6510
 Bibcode:
 2013JMP....54k3508C
 Keywords:

 Kortewegde Vries equation;
 matrix algebra;
 solitons;
 05.45.Yv;
 02.10.Yn;
 Solitons;
 Matrix theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 35Q51;
 35Q55;
 35C08;
 37K10
 EPrint:
 32 pages. Remark 6 was added, minor changes