Linearisable Abel equations and the Gurevich--Pitaevskii problem

Autor:	Opanasenko, Stanislav, Ferapontov, Evgeny
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems 33C90 34A05 34C14 35C20 35Q53 37K40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 23 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.07512 Zobrazit plný text záznamu View this record from Arxiv