Abstract:
Inverse scattering problem which is a natural two-dimensional analogue of the
Zakharov–Shabat problem is solved. Equations are considered which are integrable
with the aid of this problem.
\Bibitem{Bog87}
\by L.~V.~Bogdanov
\paper On the two-dimensional Zakharov--Shabat problem
\jour TMF
\yr 1987
\vol 72
\issue 1
\pages 155--159
\mathnet{http://mi.mathnet.ru/tmf5318}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=910489}
\zmath{https://zbmath.org/?q=an:0639.35067}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 72
\issue 1
\pages 790--793
\crossref{https://doi.org/10.1007/BF01035706}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1987M118600015}
Linking options:
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This publication is cited in the following 5 articles:
Takayuki Tsuchida, Aristophanes Dimakis, “On a (2 + 1)-dimensional generalization of the Ablowitz–Ladik lattice and a discrete Davey–Stewartson system”, J. Phys. A: Math. Theor., 44:32 (2011), 325206
Gökçe Başar, Gerald V. Dunne, “Gross-Neveu models, nonlinear Dirac equations, surfaces and strings”, J. High Energ. Phys., 2011:1 (2011)
Dmitry Zakharov, “A Discrete Analogue of the Dirac Operator and the Discrete Modified Novikov–Veselov Hierarchy”, International Mathematics Research Notices, 2010:18 (2010), 3463
I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159
I. A. Taimanov, “The Weierstrass Representation of Spheres in $\mathbb R^3$, the Willmore Numbers, and Soliton Spheres”, Proc. Steklov Inst. Math., 225 (1999), 322–343