Elbow scattering and inverse scattering applications to LKdV and KdV

DOI10.1063/1.533138zbMath0989.35116OpenAlexW2002347267MaRDI QIDQ2737828

P. C. Sabatier

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533138

zbMATH Keywords

Korteweg-de Vries equationmixed probleminverse problem method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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 (9)

Characteristic properties of the scattering data for the mKdV equation on the half-line ⋮ Generation of asymptotic solitons of the nonlinear Schrödinger equation by boundary data ⋮ Lax equations scattering and KdV ⋮ Initial value problems for integrable systems on a semi-strip ⋮ Nonlinear Schrödinger equation in a semi-strip: evolution of the Weyl-Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions ⋮ Elbow Scattering and Boundary Value Problems of NLPDE ⋮ The Ablowitz-Ladik system on the natural numbers with certain linearizable boundary conditions ⋮ Past and future of inverse problems ⋮ Solution of the Dirichlet boundary value problem for the sine-Gordon equation

Cites Work

• The solution of certain initial boundary-value problems for the linearized Korteweg—deVries equation
• On local inverse transforms
• New direct linearizations for KdV and solutions of the other Cauchy problem

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