Abstract:
The formal solution of the Gel'fand–Levitan–Marchenko equation is used to obtain the Bäcklund transformation for the class of nonlinear evolution equations that are solvable by the formalism of the inverse scattering problem for the Dirac operator with constant boundary conditions.
Citation:
V. S. Gerdjikov, P. P. Kulish, “Derivation of the Bäcklund transformation in the formalism of the inverse scattering problem”, TMF, 39:1 (1979), 69–74; Theoret. and Math. Phys., 39:1 (1979), 327–331
\Bibitem{GerKul79}
\by V.~S.~Gerdjikov, P.~P.~Kulish
\paper Derivation of the B\"acklund transformation in the formalism of the inverse scattering problem
\jour TMF
\yr 1979
\vol 39
\issue 1
\pages 69--74
\mathnet{http://mi.mathnet.ru/tmf2600}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=536467}
\transl
\jour Theoret. and Math. Phys.
\yr 1979
\vol 39
\issue 1
\pages 327--331
\crossref{https://doi.org/10.1007/BF01018944}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979HP30700007}
Linking options:
https://www.mathnet.ru/eng/tmf2600
https://www.mathnet.ru/eng/tmf/v39/i1/p69
This publication is cited in the following 11 articles:
Kitanine N., Nepomechie R.I., Reshetikhin N., “Quantum Integrability and Quantum Groups: a Special Issue in Memory of Petr P Kulish”, J. Phys. A-Math. Theor., 51:11 (2018), 110201
“Osnovnye nauchnye trudy Petra Petrovicha Kulisha”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 23, Zap. nauchn. sem. POMI, 433, POMI, SPb., 2015, 8–19
V. S. Gerdjikov, N. A. Kostov, T. I. Valchev, “Multicomponent nonlinear schrödinger equations with constant
boundary conditions”, Theoret. and Math. Phys., 159:3 (2009), 787–795
Konopelchenko, BG, “Discrete integrable systems and deformations of associative algebras”, Journal of Physics A-Mathematical and Theoretical, 42:45 (2009), 454003
Tuncay Aktosun, Cornelis van der Mee, “A unified approach to Darboux transformations”, Inverse Problems, 25:10 (2009), 105003
T. N. Arutyunyan, “O kanonicheskom operatora Diraka s chastichno zadannym spektrom”, Uch. zapiski EGU, ser. Fizika i Matematika, 1986, no. 1, 11–19
G.R.W. Quispel, F.W. Nijhoff, H.W. Capel, J.van der Linden, “Bäklund transformations and singular integral equations”, Physica A: Statistical Mechanics and its Applications, 123:2-3 (1984), 319
F.W. Nijhoff, H.W. Capel, G.L. Wiersma, G.R.W. Quispel, “Linearizing integral transform and partial difference equations”, Physics Letters A, 103:6-7 (1984), 293
V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Application of inverse scattering method to singular solutions of nonlinear equations. I”, Theoret. and Math. Phys., 53:2 (1982), 1051–1062
A. K. Prikarpatskii, “Geometrical structure and Bäcklund transformations of nonlinear evolution equations possessing a Lax representation”, Theoret. and Math. Phys., 46:3 (1981), 249–256
R. K. Bullough, P. J. Caudrey, Topics in Current Physics, 17, Solitons, 1980, 1
Citation in format AMSBIB
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