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arXiv · 1003.2892

Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation

B. Konopelchenko·L. Martinez Alonso·E. Medina
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Abstract

It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type singularities are presented.

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B. Konopelchenko, L. Martinez Alonso, E. Medina. 2010-03-15. Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation. https://doi.org/10.1088/1751-8113/43/43/434020

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