On the evolution of a reflection coefficient under the Korteweg–de Vries flow

DOI10.1063/1.2951897zbMath1152.81597OpenAlexW2057951029MaRDI QIDQ5504975

Alexei Rybkin

Publication date: 23 January 2009

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

Full work available at URL: https://doi.org/10.1063/1.2951897

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Inverse problems involving ordinary differential equations (34A55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (8)

Trace formulas for additive and non-additive perturbations ⋮ Almost periodicity in time of solutions of the KdV equation ⋮ Construction of KdV flow: a unified approach ⋮ Uniform Estimate of Potentials by Reflection Coefficients and its Application to KdV Flow ⋮ Generalized Toda flows ⋮ Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows ⋮ The effect of a positive bound state on the KdV solution: a case study ^* ⋮ Generalized reflection coefficients

Cites Work

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• On a class of solutions of KdV
• Spectral theory of canonical differential systems. Method of operator identities
• Positons: Slowly decreasing analogues of solitons
• Inverse scattering transformation for positons
• Periodic and almost-periodic potentials in inverse problems
• On spectral theory for Schrödinger operators with strongly singular potentials

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