Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-02-09
J.Math.Phys. 43 (2002) 2547-2586
Nonlinear Sciences
Exactly Solvable and Integrable Systems
LaTeX209, 43 pages
Scientific paper
10.1063/1.1466533
This paper is devoted to the systematic study of additional (non- isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type- the so called SKP_(R;M_B,M_F) models. The latter are supersymmetric extensions of ordinary constrained KP hierarchies which contain as special cases basic integrable systems such as (m)KdV, AKNS, Fordy-Kulish, Yajima- Oikawa etc.. As a first main result it is shown that any SKP_(R;M_B,M_F) hierarchy possesses two different mutually (anti-)commuting types of superloop superalgebra additional symmetries corresponding to the positive-grade and negative-grade parts of certain superloop superalgebras. The second main result is the systematic construction of the full algebra of additional Virasoro symmetries of SKP_(R;M_B,M_F) hierarchies, which requires non- trivial modifications of the Virasoro flows known from the general case of unconstrained Manin-Radul super-KP hierarchies (the latter flows do not define symmetries for constrained SKP_(R;M_B,M_F) hierarchies). As a third main result we provide systematic construction of the supersymmetric analogues of multi-component (matrix) KP hierarchies and show that the latter contain among others the supersymmetric version of Davey-Stewartson system. Finally, we present an explicit derivation of the general Darboux- B\"acklund solutions for the SKP_(R;M_B,M_F) super-tau functions (supersymmetric ``soliton''-like solutions) which preserve the additional (non-isospectral) symmetries.
Nissimov Emil
Pacheva Svetlana
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