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

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arxiv 1003.2892 v1 pith:DN72MUFG submitted 2010-03-15 nlin.SI

B. Konopelchenko , L. Martinez Alonso , E. Medina This is my paper · ORCID
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keywords solutionscriticaldckdvhierarchiescoupleddispersionlessequationeuler-poisson-darboux
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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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  1. Learning Lax Pairs: Revisiting the Classical Paradigm

    nlin.SI 2026-07 unverdicted novelty 7.0 of 10

    Lax pair compatibility underdetermines integrability, as anomalous pairs in systems like KdV still generate full conservation hierarchies through operator algebra.

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