We tackle the problem of interpreting the Darboux transformation for the KP hierarchy and its relations with the modified KP hierarchy from a geometric point of view. This is achieved by introducing the concept of a Darboux covering. We construct a Darboux covering of the KP equations and obtain a new hierarchy of equations, which we call the Darboux-KP hierarchy (DKP). We employ the DKP equations to discuss the relationships among the KP equations, the modified KP equations, and the discrete KP equations. Our approach also handles the various reductions of the KP hierarchy. We show that the KP hierarchy is a projection of the DKP, the mKP hierarchy is a DKP restriction to a suitable invariant submanifold, and that the discrete KP equations are obtained as iterations of the DKP ones.

Magri, F., Pedroni, M., Zubelli, J. (1997). On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 188(2), 305-325 [10.1007/s002200050166].

On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy

MAGRI, FRANCO;
1997

Abstract

We tackle the problem of interpreting the Darboux transformation for the KP hierarchy and its relations with the modified KP hierarchy from a geometric point of view. This is achieved by introducing the concept of a Darboux covering. We construct a Darboux covering of the KP equations and obtain a new hierarchy of equations, which we call the Darboux-KP hierarchy (DKP). We employ the DKP equations to discuss the relationships among the KP equations, the modified KP equations, and the discrete KP equations. Our approach also handles the various reductions of the KP hierarchy. We show that the KP hierarchy is a projection of the DKP, the mKP hierarchy is a DKP restriction to a suitable invariant submanifold, and that the discrete KP equations are obtained as iterations of the DKP ones.
Articolo in rivista - Articolo scientifico
Darboux transformation; KP hierarchy; modified KP hierarchy; geometric point of view; Darboux covering; Darboux-KP hierarchy
English
1997
188
2
305
325
none
Magri, F., Pedroni, M., Zubelli, J. (1997). On the geometry of Darboux transformations for the KP hierarchy and its connection with the discrete KP hierarchy. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 188(2), 305-325 [10.1007/s002200050166].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18558
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