Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

Aristophanes Dimakis ; Folkert Müller-Hoissen

Symmetry, integrability and geometry: methods and applications, Tome 5 (2009)

Résumé

Via a Cole–Hopf transformation, the multicomponent linear heat hierarchy leads to a multicomponent Burgers hierarchy. We show in particular that any solution of the latter also solves a corresponding multicomponent (potential) KP hierarchy. A generalization of the Cole–Hopf transformation leads to a more general relation between the multicomponent linear heat hierarchy and the multicomponent KP hierarchy. From this results a construction of exact solutions of the latter via a matrix linear system.

Détail

Keywords: multicomponent KP hierarchy; Burgers hierarchy; Cole–Hopf transformation; Davey–Stewartson equation; Riccati equation; dromion.

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