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arXiv · 0811.0110

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

Aristophanes Dimakis·Folkert Müller-Hoissen
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Abstract

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.

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Aristophanes Dimakis, Folkert Müller-Hoissen. 2009-01-08. Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System. https://doi.org/10.3842/sigma.2009.002

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