2022/02/15 by Stanislav Opanasenko, Opanasenko, Stanislav, E. V. Ferapontov +1
Physics and Astronomy · #33C90 #34A05 #34C14 #35C20 #35Q53 #37K40 #Advanced Fiber Laser Technologies #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2202.07512
openalex publication_date 2022/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Applying symmetry reduction to a class of 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.