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Trudy Mat. Inst. Steklova, 1999, Volume 226, Pages 49–71 (Mi tm528)  

This article is cited in 10 scientific papers (total in 10 papers)

Bäcklund and Darboux Transformations for the Nonstationary Schrödinger Equation

M. Boitia, F. Pempinellia, A. K. Pogrebkovb, B. Prinaria

a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Potentials of the nonstationary Schrödinger operator constructed by means of $n$ recursive Bäcklund transformations are studied in detail. The corresponding Darboux transformations of the Jost solutions are introduced. We show that these solutions obey modified integral equations and present their analyticity properties. Generated transformations of the spectral data are derived.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 226, 42–62

Bibliographic databases:
UDC: 501
Received in April 1999

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Bäcklund and Darboux Transformations for the Nonstationary Schrödinger Equation”, Mathematical physics. Problems of quantum field theory, Collection of papers dedicated to the 65th anniversary of academician Lyudvig Dmitrievich Faddeev, Trudy Mat. Inst. Steklova, 226, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 49–71; Proc. Steklov Inst. Math., 226 (1999), 42–62

Citation in format AMSBIB
\Bibitem{BoiPemPog99}
\by M.~Boiti, F.~Pempinelli, A.~K.~Pogrebkov, B.~Prinari
\paper B\"acklund and Darboux Transformations for the Nonstationary Schr\"odinger Equation
\inbook Mathematical physics. Problems of quantum field theory
\bookinfo Collection of papers dedicated to the 65th anniversary of academician Lyudvig Dmitrievich Faddeev
\serial Trudy Mat. Inst. Steklova
\yr 1999
\vol 226
\pages 49--71
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm528}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782552}
\zmath{https://zbmath.org/?q=an:1056.37511}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 226
\pages 42--62


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Prinari B., “On some nondecaying potentials and related Jost solutions for the heat conduction equation”, Inverse Problems, 16:3 (2000), 589–603  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Boiti M., Pempinelli F., Prinari B., Pogrebkov A.K., “Some nondecaying potentials for the nonstationary Schrodinger equation”, Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years After Needs '79, 2000, 33–41  crossref  mathscinet  zmath  isi
    3. Boiti M., Pempinelli F., Prinari B., Pogrebkov A.K., “Some nondecaying potentials for the heat conduction equation”, Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years After Needs '79, 2000, 42–50  crossref  mathscinet  zmath  isi
    4. Boiti M., Pempinelli F., Pogrebkov A.K., Prinari B., “Towards an inverse scattering theory for non–decaying potentials of the heat equation”, Inverse Problems, 17:4 (2001), 937–957  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Boiti M., Pempinelli F., Pogrebkov A.K., Prinari B., “Inverse scattering theory of the heat equation for a perturbed one–soliton potential”, Journal of Mathematical Physics, 43:2 (2002), 1044–1062  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Sakhnovich A.L., “Matrix Kadomtsev–Petviashvili equation: matrix identities and explicit non–singular solutions”, Journal of Physics A–Mathematical and General, 36:18 (2003), 5023–5033  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. Boiti, M, “Scattering transform for nonstationary Schrodinger equation with bidimensionally perturbed N-soliton potential”, Journal of Mathematical Physics, 47:12 (2006), 123510  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Boiti M., Pempinelli F., Pogrebkov A.K., “On the extended resolvent of the nonstationary Schrodinger operator for a Darboux transformed potential”, Journal of Physics A–Mathematical and General, 39:8 (2006), 1877–1898  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Sakhnovich A.L., “The time-dependent Schrodinger equation of dimension k+1: explicit and rational solutions via GBDT and multinodes”, J. Phys. A: Math. Theor., 44:47 (2011), 475201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Zhang N., Xia T., “a Hierarchy of Lattice Soliton Equations Associated With a New Discrete Eigenvalue Problem and Darboux Transformations”, Int. J. Nonlinear Sci. Numer. Simul., 16:7-8 (2015), 301–306  crossref  mathscinet  isi  elib  scopus  scopus
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