The KdV equation on a half-line ∗

  title={The KdV equation on a half-line ∗},
  author={I. T. Habibullin},
  • I. T. Habibullin
  • Published 1999
The initial boundary value problem on a half-line is integrated by means of the inverse scattering method for the KdV equation with the boundary conditions u| x=0 = a ≤ 0, u xx | x=0 = 3a 2. Time evolution of the scattering matrix is effectively defined by comparing spectra of differential operators L and A from L − A pair.