Numerical study of a multiscale expansion of the Korteweg–de Vries equation and Painlevé-II equation

DOI10.1098/rspa.2007.0249zbMath1132.35454arXiv0708.0638OpenAlexW3098871862MaRDI QIDQ5450139

Tamara Grava, Christian Klein

Publication date: 19 March 2008

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0638

zbMATH Keywords

Painlevé equationKorteweg-de Vries equationdispersive equationdouble scaling expansionsWhitham oscillatory zone

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

Complex singularities in KdV solutions, Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type, A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions, Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws, Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation, Damping to prevent the blow-up of the Korteweg-de Vries equation, An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems, Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit

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