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Linearisable Abel equations and the Gurevich-Pitaevskii problem

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TWT - Twistor theory

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 Gurevich—Pitaevskii problem, thus giving  the first term of a large time asymptotic expansion of its solution in the oscillatory (Whitham) zone. Based on joint work with S. Opanasenko.

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

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