Gentosh, O. E. Lax-integrable Laberge-Mathieu hierarchy of supersymmetric nonlinear dynamical systems and its finite-dimensional reduction of Neumann type. (Ukrainian, English) Zbl 1224.37034 Ukr. Mat. Zh. 61, No. 7, 906-921 (2009); translation in Ukr. Math. J. 61, No. 7, 1075-1092 (2009). MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{O. E. Gentosh}, Ukr. Mat. Zh. 61, No. 7, 906--921 (2009; Zbl 1224.37034); translation in Ukr. Math. J. 61, No. 7, 1075--1092 (2009) Full Text: DOI
Grigorenko, N. V. Isomonodromic deformations and the differential Galois theory. (Russian, English) Zbl 1138.34042 Ukr. Mat. Zh. 59, No. 8, 1131-1134 (2007); translation in Ukr. Math. J. 59, No. 8, 1253-1257 (2007). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 34M55 34M50 PDFBibTeX XMLCite \textit{N. V. Grigorenko}, Ukr. Mat. Zh. 59, No. 8, 1131--1134 (2007; Zbl 1138.34042); translation in Ukr. Math. J. 59, No. 8, 1253--1257 (2007) Full Text: DOI
Belokolos, E. D. Integrable superconductivity and Richardson equations. (English) Zbl 1144.37028 Ukr. Mat. Zh. 59, No. 3, 314-326 (2007) and in Ukr. Math. J. 59, No. 3, 343-360 (2007). Reviewer: A. N. Kochubei (Kyïv) MSC: 37K10 37K20 81R12 82D55 PDFBibTeX XMLCite \textit{E. D. Belokolos}, Ukr. Mat. Zh. 59, No. 3, 314--326 (2007; Zbl 1144.37028) Full Text: DOI Link
Gentosh, O. E. Compatibly bi-Hamiltonian superconformal analogues of Lax-integrable nonlinear dynamical systems. (Ukrainian, English) Zbl 1113.37052 Ukr. Mat. Zh. 58, No. 7, 887-900 (2006); translation in Ukr. Math. J. 58, No. 7, 1001-1015 (2006). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 37K30 37K10 PDFBibTeX XMLCite \textit{O. E. Gentosh}, Ukr. Mat. Zh. 58, No. 7, 887--900 (2006; Zbl 1113.37052); translation in Ukr. Math. J. 58, No. 7, 1001--1015 (2006) Full Text: DOI
Belokolos, E. D. Kinetic equations and the integrable Hamiltonian systems. (English) Zbl 1096.37038 Ukr. Mat. Zh. 57, No. 6, 731-741 (2005) and Ukr. Math. J. 57, No. 6, 869-882 (2005). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 37K10 35Q53 37K40 82C40 PDFBibTeX XMLCite \textit{E. D. Belokolos}, Ukr. Mat. Zh. 57, No. 6, 731--741 (2005; Zbl 1096.37038) Full Text: DOI
Prykarpats’kyi, A. K.; Samoilenko, V. H. Structure of binary Darboux-type transformations for Hermitian adjoint differential operators. (Ukrainian, English) Zbl 1076.37527 Ukr. Mat. Zh. 56, No. 2, 271-275 (2004); translation in Ukr. Math. J. 56, No. 2, 336-341 (2004). MSC: 37K35 37K10 PDFBibTeX XMLCite \textit{A. K. Prykarpats'kyi} and \textit{V. H. Samoilenko}, Ukr. Mat. Zh. 56, No. 2, 271--275 (2004; Zbl 1076.37527); translation in Ukr. Math. J. 56, No. 2, 336--341 (2004) Full Text: DOI
Prykarpatsky, A. K.; Hentosh, O. E. Lie-algebraic structure of \((2 + 1)\)-dimensional Lax-type integrable nonlinear dynamical systems. (English) Zbl 1075.37026 Ukr. Mat. Zh. 56, No. 7, 939-946 (2004) and Ukr. Math. J. 56, No. 7, 1117-1126 (2004). MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{A. K. Prykarpatsky} and \textit{O. E. Hentosh}, Ukr. Mat. Zh. 56, No. 7, 939--946 (2004; Zbl 1075.37026) Full Text: DOI Link
Prykarpats’kyi, Ya. A.; Samoilenko, A. M.; Samoilenko, V. H. Structure of binary transformations of Darboux type and their application to soliton theory. (Ukrainian, English) Zbl 1076.37525 Ukr. Mat. Zh. 55, No. 12, 1704-1719 (2003); translation in Ukr. Math. J. 55, No. 12, 2041-2059 (2003). MSC: 37K10 37K40 35Q51 PDFBibTeX XMLCite \textit{Ya. A. Prykarpats'kyi} et al., Ukr. Mat. Zh. 55, No. 12, 1704--1719 (2003; Zbl 1076.37525); translation in Ukr. Math. J. 55, No. 12, 2041--2059 (2003) Full Text: DOI
Sydorenko, Yu. M. Binary transformations and (2+1)-dimensional integrable systems. (Ukrainian. English summary) Zbl 1020.37049 Ukr. Mat. Zh. 54, No. 11, 1531-1550 (2002). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37K35 37K10 35Q53 35Q58 PDFBibTeX XMLCite \textit{Yu. M. Sydorenko}, Ukr. Mat. Zh. 54, No. 11, 1531--1550 (2002; Zbl 1020.37049) Full Text: DOI
Gerasymenko, V. I.; Ryabukha, T. V. Cumulant representation of solutions of the Bogolyubov chains of equations. (Ukrainian. English summary) Zbl 1027.82024 Ukr. Mat. Zh. 54, No. 10, 1313-1328 (2002). MSC: 82C05 37K10 PDFBibTeX XMLCite \textit{V. I. Gerasymenko} and \textit{T. V. Ryabukha}, Ukr. Mat. Zh. 54, No. 10, 1313--1328 (2002; Zbl 1027.82024)
Prykarpatsky, A. K.; Brzychczy, S.; Samoilenko, V. Hr. Finite-dimensional reductions of conservative dynamical systems and numerical analysis. I. (English) Zbl 0983.37083 Ukr. Math. J. 53, No. 2, 249-258 (2001) and Ukr. Mat. Zh. 53, No. 2, 220-228 (2001). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37K10 37J35 37K40 37M99 35Q53 PDFBibTeX XMLCite \textit{A. K. Prykarpatsky} et al., Ukr. Mat. Zh. 53, No. 2, 220--228 (2001; Zbl 0983.37083)
Samojlenko, A. M.; Prykarpats’kyj, Ya. A. Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable Hamiltonian systems. II. (English. Ukrainian original) Zbl 0972.37049 Ukr. Math. J. 51, No. 11, 1713-1728 (1999); translation from Ukr. Mat. Zh. 51, No. 11, 1513-1528 (1999). MSC: 37K10 37K50 37J20 PDFBibTeX XMLCite \textit{A. M. Samojlenko} and \textit{Ya. A. Prykarpats'kyj}, Ukr. Mat. Zh. 51, No. 11, 1513--1528 (1999; Zbl 0972.37049); translation from Ukr. Mat. Zh. 51, No. 11, 1513--1528 (1999) Full Text: DOI
Samojlenko, A. M.; Prykarpats’kyj, Ya. A. Investigation of invariant deformations of integral manifolds of adiabatically perturbed completely integrable Hamiltonian systems. I. (English. Ukrainian original) Zbl 0972.37048 Ukr. Math. J. 51, No. 10, 1556-1568 (1999); translation from Ukr. Mat. Zh. 51, No. 10, 1379-1390 (1999). MSC: 37K10 37K50 37J20 PDFBibTeX XMLCite \textit{A. M. Samojlenko} and \textit{Ya. A. Prykarpats'kyj}, Ukr. Mat. Zh. 51, No. 10, 1379--1390 (1999; Zbl 0972.37048); translation from Ukr. Mat. Zh. 51, No. 10, 1379--1390 (1999)
Samoilenko, A. M.; Samoilenko, V. G.; Sidorenko, Yu. M. Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced systems. (English. Ukrainian original) Zbl 0935.37035 Ukr. Math. J. 51, No. 1, 86-106 (1999); translation from Ukr. Mat. Zh. 51, No. 1, 78-97 (1999). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37K10 81T10 PDFBibTeX XMLCite \textit{A. M. Samoilenko} et al., Ukr. Mat. Zh. 51, No. 1, 78--97 (1999; Zbl 0935.37035); translation from Ukr. Mat. Zh. 51, No. 1, 78--97 (1999)
Samoilenko, V. G.; Sidorenko, Yu. M. Hierarchy of the Burgers matrix equations and integrable reductions in the Davey-Stewartson system. (Ukrainian) Zbl 0913.58030 Ukr. Mat. Zh. 50, No. 2, 252-263 (1998). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37J35 37K10 35C05 58J72 PDFBibTeX XMLCite \textit{V. G. Samoilenko} and \textit{Yu. M. Sidorenko}, Ukr. Mat. Zh. 50, No. 2, 252--263 (1998; Zbl 0913.58030) Full Text: DOI
Bulitko, V. K.; Bulitko, V. V. On a criterion of \({\mathcal N}P\)-completeness. (English. Russian original) Zbl 0968.68515 Ukr. Math. J. 50, No. 12, 1924-1928 (1998); translation from Ukr. Mat. Zh. 50, No. 12, 1686-1691 (1998). MSC: 68Q15 PDFBibTeX XMLCite \textit{V. K. Bulitko} and \textit{V. V. Bulitko}, Ukr. Mat. Zh. 50, No. 12, 1 (1998; Zbl 0968.68515); translation from Ukr. Mat. Zh. 50, No. 12, 1686--1691 (1998) Full Text: DOI
Tadzima, S. Perturbed Lamé equation and the Buslaev phase. (English. Russian original) Zbl 0940.34071 Ukr. Math. J. 50, No. 12, 1908-1916 (1998); translation from Ukr. Mat. Zh. 50, No. 12, 1673-1679 (1998). Reviewer: I.O.Parasyuk (Kyïv) MSC: 34M55 81Q20 34M30 34M25 PDFBibTeX XMLCite \textit{S. Tadzima}, Ukr. Mat. Zh. 50, No. 12, 1673--1679 (1998; Zbl 0940.34071); translation from Ukr. Mat. Zh. 50, No. 12, 1673--1679 (1998) Full Text: DOI
Kondrat’ev, A. Yu.; Ènol’skiĭ, V. Z. Jacobi polynomials and Lax representation for completely integrable dynamical systems. (English. Russian original) Zbl 0866.35106 Ukr. Math. J. 46, No. 8, 1198-1201 (1994); translation from Ukr. Mat. Zh. 46, No. 8, 1088-1091 (1994). MSC: 35Q53 37J35 37K10 PDFBibTeX XMLCite \textit{A. Yu. Kondrat'ev} and \textit{V. Z. Ènol'skiĭ}, Ukr. Mat. Zh. 46, No. 8, 1088--1091 (1994; Zbl 0866.35106); translation from Ukr. Mat. Zh. 46, No. 8, 1088--1091 (1994) Full Text: DOI
Kujbida, V. S.; Prikarpatskij, A. K. Parametric integrability in the sense of Lax of nonlinear dynamical systems and the splitting problem of multisoliton separatrix manifolds. (Russian) Zbl 0763.35079 Ukr. Mat. Zh. 44, No. 3, 365-379 (1992). Reviewer: A.Doktor (Praha) MSC: 35Q53 37J35 37K10 58J45 PDFBibTeX XMLCite \textit{V. S. Kujbida} and \textit{A. K. Prikarpatskij}, Ukr. Mat. Zh. 44, No. 3, 365--379 (1992; Zbl 0763.35079)
Siroïd, I.-P. P. Matrix solutions of the equation \({\mathfrak B}U_ t = -U_{xx} + 2U^ 3 + {\mathfrak B}[U_ x,U] + 4cU\): Extension of the inverse scattering method. (English. Ukrainian original) Zbl 0784.35109 Ukr. Math. J. 44, No. 9, 1156-1166 (1992); translation from Ukr. Mat. Zh. 44, No. 9, 1264-1275 (1992). Reviewer: L.A.Sakhnovich (Odessa) MSC: 35Q55 37J35 37K10 35R30 PDFBibTeX XMLCite \textit{I. P. P. Siroïd}, Ukr. Mat. Zh. 44, No. 9, 1264--1275 (1992; Zbl 0784.35109); translation from Ukr. Mat. Zh. 44, No. 9, 1264--1275 (1992)
Prikarpatskij, A. K.; Fil’, B. M. Category of topological jet-manifolds and certain applications in the theory of nonlinear infinite-dimensional dynamical systems. (English. Ukrainian original) Zbl 0783.58006 Ukr. Math. J. 44, No. 9, 1136-1148 (1992); translation from Ukr. Mat. Zh. 44, No. 9, 1242-1256 (1992). Reviewer: A.Klíč (Praha) MSC: 58A20 37J35 37K10 58D15 58A50 17A70 PDFBibTeX XMLCite \textit{A. K. Prikarpatskij} and \textit{B. M. Fil'}, Ukr. Mat. Zh. 44, No. 9, 1242--1256 (1992; Zbl 0783.58006); translation from Ukr. Mat. Zh. 44, No. 9, 1242--1256 (1992)
Balins’kij, A. I. On discrete models on one-dimensional lattices with specified Lie algebra of symmetries. (English. Ukrainian original) Zbl 0791.58049 Ukr. Math. J. 44, No. 9, 1069-1072 (1992); translation from Ukr. Mat. Zh. 44, No. 9, 1170-1174 (1992). MSC: 37J35 37K10 37N99 81U20 PDFBibTeX XMLCite \textit{A. I. Balins'kij}, Ukr. Mat. Zh. 44, No. 9, 1170--1174 (1992; Zbl 0791.58049); translation from Ukr. Mat. Zh. 44, No. 9, 1170--1174 (1992) Full Text: DOI
Samojlenko, V. G.; Pritula, N. N.; Sujarov, U. S. Analysis of complete integrability of the inverse Korteweg-de Vries equation. (Russian) Zbl 0749.35049 Ukr. Mat. Zh. 43, No. 9, 1239-1248 (1991). Reviewer: B.G.Konopelchenko (Novosibirsk) MSC: 35Q53 37J35 37K10 PDFBibTeX XMLCite \textit{V. G. Samojlenko} et al., Ukr. Mat. Zh. 43, No. 9, 1239--1248 (1991; Zbl 0749.35049)
Bogolyubov, N. N. jun.; Prikarpatskij, A. K. A bilocal periodic problem for Sturm-Liouville and Dirac operators and some applications in the theory of nonlinear dynamical systems. I. (Russian) Zbl 0705.35114 Ukr. Mat. Zh. 42, No. 6, 794-800 (1990). Reviewer: B.A.Malomed MSC: 35Q40 35Q58 34L40 37J35 37K10 PDFBibTeX XMLCite \textit{N. N. Bogolyubov jun.} and \textit{A. K. Prikarpatskij}, Ukr. Mat. Zh. 42, No. 6, 794--800 (1990; Zbl 0705.35114) Full Text: DOI
Samojlenko, V. G. Differential-geometric structure and spectral properties of nonlinear completely integrable dynamical systems of Mel’nikov type. (Russian) Zbl 0704.58023 Ukr. Mat. Zh. 42, No. 5, 655-659 (1990). Reviewer: Ch.Athorne MSC: 37J35 37K10 35Q53 PDFBibTeX XMLCite \textit{V. G. Samojlenko}, Ukr. Mat. Zh. 42, No. 5, 655--659 (1990; Zbl 0704.58023)
Samojlenko, V. Gr.; Fil’, B. N. Algebras of symmetries of completely integrable dynamical systems. (Russian) Zbl 0654.58019 Ukr. Mat. Zh. 40, No. 2, 192-198 (1988). Reviewer: G.-Z.Tu MSC: 37J35 37K10 17B65 35Q99 PDFBibTeX XMLCite \textit{V. Gr. Samojlenko} and \textit{B. N. Fil'}, Ukr. Mat. Zh. 40, No. 2, 192--198 (1988; Zbl 0654.58019)
Teplinskiĭ, Yu. V. On the existence of an invariant toroidal manifold for a countable system of differential equations with instantaneous change. (Über die Existenz einer invarianten toroidalen Mannigfaltigkeit eines abzählbaren Systems von Differentialgleichungen mit momentaner Änderung.) (Russian) Zbl 0388.58021 Ukr. Mat. Zh. 29, 835-841 (1977). MSC: 37C80 37J35 37K10 34A34 PDFBibTeX XMLCite \textit{Yu. V. Teplinskiĭ}, Ukr. Mat. Zh. 29, 835--841 (1977; Zbl 0388.58021)