Airy and Painlevé asymptotics for the mKdV equation

DOI10.1112/jlms.12265zbMath1443.37054arXiv1808.08408OpenAlexW3105841495MaRDI QIDQ5108147

Jonatan Lenells, Christophe Charlier

Publication date: 29 April 2020

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.08408

zbMATH Keywords

modified Korteweg-de Vries equationPainlevé II equationPainlevé sector

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items

Higher Order Airy and Painlevé Asymptotics for the mKdV Hierarchy, Painlevé-type asymptotics of an extended modified KdV equation in transition regions, Long-time asymptotic behavior for the matrix modified Korteweg-de Vries equation, Painlevé asymptotics for the coupled Sasa-Satsuma equation, A two-component Sasa-Satsuma equation: large-time asymptotics on the line, The defocusing nonlinear Schrödinger equation with a nonzero background: Painlevé asymptotics in two transition regions, Asymptotics for the Sasa-Satsuma equation in terms of a modified Painlevé II transcendent

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