Caustics in 1+1 integrable systems

DOI10.1063/1.530495zbMath0807.35135OpenAlexW2050776189MaRDI QIDQ4314264

Alexander V. Kitaev

Publication date: 1 March 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530495

zbMATH Keywords

inverse scattering transformsecond Painlevé equationrapidly decaying solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (13)

Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems ⋮ Emptiness formation probability of the six-vertex model and the sixth Painlevé equation ⋮ Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1 ⋮ Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as \(|x|\to\infty\) ⋮ Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation ⋮ On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations ⋮ Unnamed Item ⋮ Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation ⋮ ``Quantizations of higher Hamiltonian analogues of the Painlevé I and Painlevé II equations with two degrees of freedom ⋮ Existence and uniqueness of Tronquée solutions of the fourth-order Jimbo-Miwa second Painlevé equation ⋮ Asymptotics of oscillatory Riemann–Hilbert problems ⋮ Small-amplitude dispersion oscillations on the background of the nonlinear geometric optic approximation

Cites Work

• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Self-similar solutions of the modified nonlinear Schrödinger equation
• Justification of the asymptotic formulas obtained by the isomonodromic deformation method
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Nonlinear Cusped Caustics for Dispersive Waves
• Nonlinear effects upon waves near caustics

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