Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfaces

DOI10.1007/BF01078940zbMath0716.35073OpenAlexW2010844941MaRDI QIDQ753025

Ramil' F. Bikbaev

Publication date: 1989

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01078940

zbMATH Keywords

Cauchy problemWhitham deformation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (5)

Parametric resonance in integrable systems and averaging on Riemann surfaces ⋮ Dynamic soliton–mean flow interaction with non-convex flux ⋮ Initial-boundary value problem for stimulated Raman scattering model: solvability of Whitham type system of equations arising in long-time asymptotic analysis ⋮ Undular bore transition in bi-directional conservative wave dynamics ⋮ Asymptotic expansion of the solution to the Cauchy problem for the Volterra chain with a step-like initial condition

Cites Work

• Asymptotics for \(t\to \infty\) of the solution to the Cauchy problem for the Korteweg-de Vries equation in the class of potentials with finite-gap behavior as \(x\to \pm \infty\)
• Solitons of the nonlinear Schrödinger equation generated by the continuum
• The small dispersion limit of the Korteweg-de Vries equation. III
• Long Time Asymptotics of the Korteweg-de Vries Equation
• The hyperbolic nature of the zero dispersion Kdv limit
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfaces