The KdV equation on a half-line

1999/10/08 by I. T. Habibullin, Habibullin, I. T., А. Н. Вильданов +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9910002

14 pages. Some revisions are made and more detailes are worked out in comparison with the previous version (which was of 11 pages), pictures are added

arxiv created 1999/11/12 · arxiv updated 2009/11/30

Abstract

The initial boundary value problem on a half-line for the KdV equation with the boundary conditions u|_x=0=a≤0, u_xx|_x=0=3a² is integrated by means of the inverse scattering method. In order to find the time evolution of the scattering matrix it turned out to be sufficient to solve the Riemann problem on a hyperelliptic curve of genus two, where the conjugation matrices are effectively defined by initial data.

Related

• Initial boundary value problem on a half-line for the MKdV equation
• The KdV equation on the half-line: The Dirichlet to Neumann map
• Characteristic properties of the scattering data for the mKdV equation on the half-line
• Regular Global Solutions for A Generalized KdV Equation Posed on A\n Half-Line
• The generalized Korteweg-de Vries equation on the half line