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Sergey Kabanikhin, Maxim Shishlenin, Nikita Novikov, Nikita Prokhoshin, “Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations”, Mathematics, 11:21 (2023), 4458
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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
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Evgeny Lakshtanov, Boris Vainberg, “Recovery of L
p
-potential in the plane”, Journal of Inverse and Ill-posed Problems, 25:5 (2017), 633
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A. D. Agaltsov, R. G. Novikov, “Riemann–Hilbert problem approach for two-dimensional flow inverse scattering”, Journal of Mathematical Physics, 55:10 (2014)
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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)
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R. G. Novikov, “The $\bar{\partial}$ -Approach to Monochromatic Inverse Scattering in Three Dimensions”, J Geom Anal, 18:2 (2008), 612
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Rob Hagemans, Jean-Sébastien Caux, “Deformed strings in the Heisenberg model”, J. Phys. A: Math. Theor., 40:49 (2007), 14605
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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
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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
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V. A. Burov, O. D. Rumyantseva, “Uniqueness and stability of the solution to an inverse acoustic scattering problem”, Acoust. Phys., 49:5 (2003), 496
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R G Novikov, “On the range characterization for the two-dimensional attenuated x-ray transformation”, Inverse Problems, 18:3 (2002), 677
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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
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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
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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
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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
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V. D. Lipovskii, A. V. Shirokov, “$2+1$ Toda chain. I. Inverse scattering method”, Theoret. and Math. Phys., 75:3 (1988), 555–566
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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
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R. G. Novikov, G. M. Henkin, “The $\bar\partial$-equation in the multidimensional inverse scattering problem”, Russian Math. Surveys, 42:3 (1987), 109–180
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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
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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