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Linearisable Abel equations and the Gurevich-Pitaevskii problem

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HY2W01 - Modulation theory and dispersive shock waves

Applying symmetry reduction to a class of SL(2;R)-invariant third-order ODEs, we obtain Abel equations whose general solution can be parametrised by hypergeometric functions. Particular case of this construction provides a general parametric solution to the Kudashev equation, an ODE arising in the asymptotic analysis of a simultaneous solution to the KdV equation and the stationary part of its higher non-autonomous symmetry.

This talk is part of the Isaac Newton Institute Seminar Series series.

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