Scattering and inverse scattering for a leftdefinite SturmLiouville problem
(2012) In Journal of Differential Equations 253(8). p.23802419 Abstract
 This work develops a scattering and an inverse scattering theory for the SturmLiouville equation u '' qu = lambda wu where w may change sign but q >= 0. Thus the lefthand side of the equation gives rise to a positive quadratic form and one is led to a leftdefinite 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 PaleyWiener theorem linking growth properties of transforms with support properties of functions. One motivation for this investigation comes from the CamassaHolm equation for which the solution of the Cauchy problem can be achieved by the inverse scattering transform for u '' + 1/4 u =... (More)
 This work develops a scattering and an inverse scattering theory for the SturmLiouville equation u '' qu = lambda wu where w may change sign but q >= 0. Thus the lefthand side of the equation gives rise to a positive quadratic form and one is led to a leftdefinite 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 PaleyWiener theorem linking growth properties of transforms with support properties of functions. One motivation for this investigation comes from the CamassaHolm 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3055579
 author
 Bennewitz, Christer ^{LU} ; Brown, B. M. and Weikard, R.
 organization
 publishing date
 2012
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Scattering theory, Inverse scattering theory, Leftdefinite problems, CamassaHolm equation
 in
 Journal of Differential Equations
 volume
 253
 issue
 8
 pages
 2380  2419
 publisher
 Elsevier
 external identifiers

 wos:000307604500002
 scopus:84864309254
 ISSN
 00220396
 DOI
 10.1016/j.jde.2012.06.016
 language
 English
 LU publication?
 yes
 id
 6b25344d85734c97903c469d7227f405 (old id 3055579)
 date added to LUP
 20120925 14:01:56
 date last changed
 20180107 03:11:57
@article{6b25344d85734c97903c469d7227f405, abstract = {This work develops a scattering and an inverse scattering theory for the SturmLiouville equation u '' qu = lambda wu where w may change sign but q >= 0. Thus the lefthand side of the equation gives rise to a positive quadratic form and one is led to a leftdefinite 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 PaleyWiener theorem linking growth properties of transforms with support properties of functions. One motivation for this investigation comes from the CamassaHolm 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.}, author = {Bennewitz, Christer and Brown, B. M. and Weikard, R.}, issn = {00220396}, keyword = {Scattering theory,Inverse scattering theory,Leftdefinite problems,CamassaHolm equation}, language = {eng}, number = {8}, pages = {23802419}, publisher = {Elsevier}, series = {Journal of Differential Equations}, title = {Scattering and inverse scattering for a leftdefinite SturmLiouville problem}, url = {http://dx.doi.org/10.1016/j.jde.2012.06.016}, volume = {253}, year = {2012}, }