R. G. Novikov, “Construction of two-dimensional Schrödinger operator with given scattering amplitude at fixed energy”, TMF, 66:2 (1986), 234–240; Theoret. and Math. Phys., 66:2 (1986), 154

Citation in format AMSBIB

\Bibitem{Nov86}

\by R.~G.~Novikov

\paper Construction of two-dimensional Schr\"odinger operator with given scattering amplitude at fixed energy

\jour TMF

\yr 1986

\vol 66

\issue 2

\pages 234--240

\mathnet{http://mi.mathnet.ru/tmf4619}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=838277}

\zmath{https://zbmath.org/?q=an:0615.35023}

\transl

\jour Theoret. and Math. Phys.

\yr 1986

\vol 66

\issue 2

\pages 154--158

\crossref{https://doi.org/10.1007/BF01017767}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986E417400008}

This publication is cited in the following 21 articles:

Sergey Kabanikhin, Maxim Shishlenin, Nikita Novikov, Nikita Prokhoshin, “Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations”, Mathematics, 11:21 (2023), 4458
A. D. Agaltsov, R. G. Novikov, “Examples of solution of the inverse scattering problem and the equations of the Novikov–Veselov hierarchy from the scattering data of point potentials”, Russian Math. Surveys, 74:3 (2019), 373–386
Evgeny Lakshtanov, Boris Vainberg, “Recovery of L
p -potential in the plane”, Journal of Inverse and Ill-posed Problems, 25:5 (2017), 633
A. D. Agaltsov, R. G. Novikov, “Riemann–Hilbert problem approach for two-dimensional flow inverse scattering”, Journal of Mathematical Physics, 55:10 (2014)
V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “Two-dimensional stationary Schrödinger equation via the ∂¯-dressing method: New exactly solvable potentials, wave functions, and their physical interpretation”, Journal of Mathematical Physics, 51:9 (2010)
R. G. Novikov, “The $\bar{\partial}$ -Approach to Monochromatic Inverse Scattering in Three Dimensions”, J Geom Anal, 18:2 (2008), 612
Rob Hagemans, Jean-Sébastien Caux, “Deformed strings in the Heisenberg model”, J. Phys. A: Math. Theor., 40:49 (2007), 14605
N. V. Alekseenko, “Solution of the Three-Dimensional Inverse Acoustic Scattering Problem on the Basis of the Novikov–Henkin Algorithm”, Acoust. Phys., 51:4 (2005), 367
V. A. Burov, I. M. Grishina, O. I. Lapshenkina, S. A. Morozov, O. D. Rumyantseva, E. G. Sukhov, “Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities”, Acoust. Phys., 49:6 (2003), 627
V. A. Burov, O. D. Rumyantseva, “Uniqueness and stability of the solution to an inverse acoustic scattering problem”, Acoust. Phys., 49:5 (2003), 496
R G Novikov, “On the range characterization for the two-dimensional attenuated x-ray transformation”, Inverse Problems, 18:3 (2002), 677
P. G. Grinevich, “Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity”, Russian Math. Surveys, 55:6 (2000), 1015–1083
A. S. Starkov, “Transform operators in a two-dimensional inverse problem for a finite domain”, J. Math. Sci. (New York), 91:2 (1998), 2866–2872
A.G. Ramm, “Can a constant be the fixed-energy scattering amplitude for an integrable local potential?”, Physics Letters A, 154:1-2 (1991), 35
R. G. Novikov, “Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$”, Funct. Anal. Appl., 22:4 (1988), 263–272
V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. I. Inverse scattering method”, Theoret. and Math. Phys., 75:3 (1988), 555–566
A. P. Katchalov, Ya. V. Kurylev, “Asymptotics of the Jost-function for the two-dimensional Schrödinger operator”, J. Soviet Math., 55:3 (1991), 1712–1717
R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180
P. G. Grinevich, “Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy”, Theoret. and Math. Phys., 69:2 (1986), 1170–1172
P. G. Grinevich, S. V. Manakov, “Inverse scattering problem for the two-dimensional Schrödinger operator, the $\bar\partial$-method and nonlinear equations”, Funct. Anal. Appl., 20:2 (1986), 94–103