| Title | Scattering and inverse scattering for a left-definite Sturm-Liouville problem |
| Authors | Christer Bennewitz, B. M. Brown, R. Weikard |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Differential Equations |
| Year | 2012 |
| Volume | 253 |
| Issue | 8 |
| Pages | 2380 - 2419 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Academic Press Inc Elsevier Science |
| Abstract English | This work develops a scattering and an inverse scattering theory for the Sturm-Liouville equation u '' qu = lambda wu 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 '' + 1/4 u = lambda wu. (c) 2012 Elsevier Inc. All rights reserved. |
| Keywords | Scattering theory, Inverse scattering theory, Left-definite problems, Camassa-Holm equation, |
| ISBN/ISSN/Other | ISSN: 0022-0396 |
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