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Linearizable Abel equations and the Gurevich–Pitaevskii problem

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posted on 2023-03-22, 09:35 authored by Stanislav Opanasenko, Evgeny FerapontovEvgeny Ferapontov

Applying symmetry reduction to a class of (Formula presented.) -invariant third-order ordinary differential equations (ODEs), we obtain Abel equations whose general solution can be parameterized 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.

Funding

Natural Sciences and Engineering Research Council of Canada

Russian Science Foundation

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Studies in Applied Mathematics

Volume

150

Issue

3

Pages

607-628

Publisher

Wiley

Version

  • VoR (Version of Record)

Rights holder

© The Authors

Publisher statement

This is an open access article under the terms of the Creative Commons Attribution (https://creativecommons.org/licenses/by/4.0/) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Acceptance date

2022-11-18

Publication date

2022-12-15

Copyright date

2022

ISSN

0022-2526

eISSN

1467-9590

Language

  • en

Depositor

Deposit date: 13 February 2023

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