Scattering and inverse scattering for a leftdefinite SturmLiouville problem
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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.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Pages (fromto)  23802419 
Journal  Journal of Differential Equations 
Volume  253 
Issue number  8 
Publication status  Published  2012 
Publication category  Research 
Peerreviewed  Yes 