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

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Trudy Matematicheskogo Instituta imeni V.A. 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. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov^b, B. Prinari^a

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

Full-text PDF (2224 kB) Citations (10)

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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.

Received in April 1999

Bibliographic databases:

Document Type: Article

UDC: 501

Language: Russian

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://mathscinet.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

Linking options:

https://www.mathnet.ru/eng/tm528

https://www.mathnet.ru/eng/tm/v226/p49

This publication is cited in the following 10 articles:

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
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
Boiti, M, “Scattering transform for nonstationary Schrodinger equation with bidimensionally perturbed N-soliton potential”, Journal of Mathematical Physics, 47:12 (2006), 123510
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
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
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
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
Prinari B., “On some nondecaying potentials and related Jost solutions for the heat conduction equation”, Inverse Problems, 16:3 (2000), 589–603
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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