LDR 03199     2200373   4500
010    _a9781470420260
       _bbr.
011    _a0065-9266
090    _a17010
101    _aeng
102    _aUS
100    _a20150209              frey50       
200    _aAn inverse spectral problem related to the Geng-Xue two-component Peakon equation
       _bM
       _fHans Lundmark, Jacek Szmigielski
210    _aProvidence (R.I.)
       _cAmerican Mathematical Society
       _d2016
215    _a1 vol. (VII-87 p.)
       _d26
       _cill.
225    _9170211
       _aMemoirs of the American Mathematical Society
       _v1155
       _x0065-9266
320    _aBibliogr. p. [85]-87. Index
330    _aAuthors’ abstract: We solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a ‘discrete cubic string’ type – a nonselfadjoint generalization of a classical inhomogeneous string – but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein’s solution of the inverse problem for the Stieltjes string.
410    _9170209
       _aAMS
       _tMemoirs of the American Mathematical Society
       _x0065-9266
676    _a2010
686    _20
       _9163755
       _a35Q53
       _bPartial differential equations -- Equations of mathematical physics and other areas of application
       _xKdV-like equations (Korteweg-de Vries)
686    _20
       _9163471
       _a34L25
       _bOrdinary differential equations -- Ordinary differential operators
       _xScattering theory, inverse scattering
686    _20
       _9163738
       _a35P05
       _bPartial differential equations -- Spectral theory and eigenvalue problems
       _xGeneral topics in linear spectral theory
686    _20
       _9163754
       _a35Q51
       _bPartial differential equations -- Equations of mathematical physics and other areas of application
       _xSoliton-like equations
686    _20
       _9163792
       _a35R30
       _bPartial differential equations -- Miscellaneous topics
       _xInverse problems
700    _4070
       _aLundmark
       _bHans
       _f1970-
       _9183282
701    _4070
       _aSzmigielski
       _bJacek
       _f1954-
       _9183283
856    _uhttps://zbmath.org/?q=an:1375.34030
       _zzbMath
856    _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=3545110
       _zMSN
856    _uhttps://arxiv.org/pdf/1304.0854.pdf
       _zArXiv
856    _uhttp://www.ams.org/books/memo/1155/
       _zAMS-résumé
905    _aaw
       _b2018
906    _aaw
       _b2018-11-27
001     17010
995    _f12535-01
       _xachat
       _918695
       _cCMI
       _20
       _kSéries AMS
       _o0
       _eCouloir
       _bCMI
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