Scattering and inverse scattering for a left-definite Sturm-Liouville problem

Academic Article


  • This work develops a scattering and an inverse scattering theory for the Sturm-Liouville equation -u"+qu=λwu where w may change sign but q≥ 0. Thus the left-hand side of the equation gives rise to a positive quadratic form and one is led to a left-definite spectral problem. The crucial ingredient of the approach is a generalized transform built on the Jost solutions of the problem and hence termed the Jost transform and the associated Paley-Wiener theorem linking growth properties of transforms with support properties of functions.One motivation for this investigation comes from the Camassa-Holm equation for which the solution of the Cauchy problem can be achieved by the inverse scattering transform for -u"+14u=λwu. © 2012 Elsevier Inc.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Bennewitz C; Brown BM; Weikard R
  • Start Page

  • 2380
  • End Page

  • 2419
  • Volume

  • 253
  • Issue

  • 8