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Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system

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Müller-Hoissen,  Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Dimakis, A., & Müller-Hoissen, F. (2009). Multicomponent Burgers and KP hierarchies, and solutions from a matrix linear system. Sigma, 5: 002. doi:10.3842/SIGMA.2009.002.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1331-3
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.