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arXiv · 2202.07512

Linearisable Abel equations and the Gurevich--Pitaevskii problem

Stanislav Opanasenko·Evgeny Ferapontov
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Abstract

Applying symmetry reduction to a class of $\mathrm{SL}(2,\mathbb R)$-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.

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Stanislav Opanasenko, Evgeny Ferapontov. 2022-02-15. Linearisable Abel equations and the Gurevich--Pitaevskii problem. https://arxiv.org/abs/2202.07512

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