Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrant

DOI10.1063/1.4980015zbMath1364.35315arXiv1212.1730OpenAlexW3101198401MaRDI QIDQ5738679

Andrey Melnikov

Publication date: 12 June 2017

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

Full work available at URL: https://arxiv.org/abs/1212.1730

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations of ordinary differential equations (34D10) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (4)

Solution of the Korteweg-de Vries equation on the line with analytic initial potential ⋮ Classification of KdV vessels with constant parameters and two dimensional outer space ⋮ Solitonic combinations, commuting nonselfadjoint operators, and applications ⋮ Solution of the Boussinesq equation using evolutionary vessels

Cites Work

• Finite-dimensional Sturm-Liouville vessels and their tau functions
• A Schur algorithm for transfer function of over-determined conservative systems, invariant in one direction
• Interpolation of rational matrix functions
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Livsic-type determinantal representations and hyperbolicity
• Schur algorithm in the class \({\mathcal{SI}}\) of \(J\)-contractive functions intertwining solutions of linear differential equations
• On construction of solutions of evolutionary nonlinear Schrödinger equation
• Inverse scattering of canonical systems and their evolution
• Solution of the Korteweg-de Vries equation on the line with analytic initial potential
• Method for Solving the Korteweg-deVries Equation
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Construction of a Sturm-Liouville vessel using Gelfand-Levitan theory. On solution of the Korteweg-de Vries equation in the first quadrant