Analitical theory of differential equations, isomonodromic deformations, Riemann-Hilbert problem.
Main publications:
V. Poberezhny, “General linear problem of the isomonodromic deformation of fuchsian system”, Math. Notes, 81:3-4 (2007), 529–542
V. Poberezhny, “On the Painlevé property of isomonodromic deformations of Fuchsian systems”, Acta Appl. Math., 101:1-3 (2008), 255–263
R. Gontsov, V.Poberezhny, “Various versions of the Riemann-Hilbert problem for linear differential equations”, Rus. Math. Surveys, 63:4 (2008), 603–639
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Darboux transformations for the discrete versions of the KP and strict KP hierarchies”, TMF, 221:3 (2024), 503–522; Theoret. and Math. Phys., 221:3 (2024), 2031–2048
2022
2.
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Minimal realizations and scaling invariance of the discrete KP hierarchy and its strict version”, TMF, 213:1 (2022), 41–56; Theoret. and Math. Phys., 213:1 (2022), 1348–1361
2020
3.
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Extensions of the discrete KP hierarchy and its strict version”, TMF, 204:3 (2020), 367–382; Theoret. and Math. Phys., 204:3 (2020), 1140–1153
2019
4.
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Strict versions of integrable hierarchies in pseudodifference operators and the related Cauchy problems”, TMF, 198:2 (2019), 225–245; Theoret. and Math. Phys., 198:2 (2019), 197–214
A. A. Matveeva, V. A. Poberezhnyi, “The One-Dimensional Riemann Problem on an Elliptic Curve”, Mat. Zametki, 101:1 (2017), 91–100; Math. Notes, 101:1 (2017), 115–122
R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Uspekhi Mat. Nauk, 66:1(397) (2011), 65–110; Russian Math. Surveys, 66:1 (2011), 63–105
G. F. Helminck, V. A. Poberezhnyi, “Moving poles of meromorphic linear systems on $\mathbb P^1(\mathbb C)$ in the complex plane”, TMF, 165:3 (2010), 472–487; Theoret. and Math. Phys., 165:3 (2010), 1637–1649
R. R. Gontsov, V. A. Poberezhnyi, “Various versions of the Riemann–Hilbert problem for linear differential equations”, Uspekhi Mat. Nauk, 63:4(382) (2008), 3–42; Russian Math. Surveys, 63:4 (2008), 603–639
V. A. Poberezhnyi, “General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems”, Mat. Zametki, 81:4 (2007), 599–613; Math. Notes, 81:4 (2007), 529–542
V. A. Poberezhnyi, “Special Monodromy Groups and the Riemann–Hilbert Problem for the Riemann Equation”, Mat. Zametki, 77:5 (2005), 753–767; Math. Notes, 77:5 (2005), 695–707
A. V. Chernavskii, V. P. Leksin, M. Butuzov, I. V. Vyugin, R. R. Gontsov, V. A. Poberezhnyi, Yu. S. Ilyashenko, A. G. Sergeev, S. P. Konovalov, “Reminiscences about Andrei Andreevich Bolibrukh”, Uspekhi Mat. Nauk, 59:6(360) (2004), 207–215; Russian Math. Surveys, 59:6 (2004), 1213–1224
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