A. S. Popov, I. V. Shirokov, “Star product on the Lie coalgebra and its application for calculation of quantum integrals of motion”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(30) (2013), 379–386
A. I. Breev, I. V. Shirokov, A. A. Magazev, “Vacuum polarization of a scalar field on Lie groups and homogeneous spaces”, Theoret. and Math. Phys., 167:1 (2011), 468–483
I. V. Shirokov, “Symmetric cipher on the base of non-commutative algebra of polynomials”, Prikl. Diskr. Mat., 2010, no. supplement № 3, 35–36
I. V. Shirokov, A. V. Prolubnikov, “Algorithms for the graph isomorphism problem based on graph deregularisation”, Prikl. Diskr. Mat., 2009, no. supplement № 1, 101–102
S. P. Baranovskii, I. V. Shirokov, “Deformations of vector fields and canonical coordinates on coadjoint orbits”, Siberian Math. J., 50:4 (2009), 580–586
M. M. Goncharovskiy, I. V. Shirokov, “An integrable class of differential equations with nonlocal nonlinearity on Lie groups”, Theoret. and Math. Phys., 161:3 (2009), 1604–1615
O. L. Kurnyavko, I. V. Shirokov, “Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields”, Theoret. and Math. Phys., 156:2 (2008), 1169–1179
A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, “Integrable magnetic geodesic flows on Lie groups”, Theoret. and Math. Phys., 156:2 (2008), 1127–1141
I. V. Shirokov, “Differential invariants of the transformation group of a homogeneous space”, Siberian Math. J., 48:6 (2007), 1127–1140
A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49
A. A. Magazev, I. V. Shirokov, “Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group”, Theoret. and Math. Phys., 136:3 (2003), 1212–1224
S. P. Baranovskii, I. V. Shirokov, “Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces”, Theoret. and Math. Phys., 135:1 (2003), 510–519
S. P. Baranovskii, V. V. Mikheyev, I. V. Shirokov, “Quantum Hamiltonian Systems on K-Orbits: Semiclassical Spectrum of the Asymmetric Top”, Theoret. and Math. Phys., 129:1 (2001), 1311–1319
I. V. Shirokov, “Identities and Invariant Operators on Homogeneous Spaces”, Theoret. and Math. Phys., 126:3 (2001), 326–338
I. V. Shirokov, “Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups”, Theoret. and Math. Phys., 123:3 (2000), 754–767
I. V. Shirokov, “Investigation of the stability of solutions of differential equations that admit a transitive symmetry group”, Russian Math. (Iz. VUZ), 43:3 (1999), 56–62
A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Local symmetry algebra of Shrödinger equation for Hydrogen atom”, Theoret. and Math. Phys., 106:2 (1996), 227–236
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration method for linear partial differential equations. Functional algebras and dimensional reduction”, Theoret. and Math. Phys., 106:1 (1996), 1–10
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, Theoret. and Math. Phys., 104:2 (1995), 921–934
A. V. Shapovalov, I. V. Shirokov, “Symmetry algebras of linear differential equations”, Theoret. and Math. Phys., 92:1 (1992), 697–703
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Generation of new exactly solvable potentials of a nonstationary Schrödinger equation”, Theoret. and Math. Phys., 87:3 (1991), 635–640
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Identities on solutions of the wave equation in the enveloping algebra of the conformal group”, Theoret. and Math. Phys., 83:1 (1990), 347–353
O. L. Kurnyavko, I. V. Shirokov, “Construction of first-order invariant differential operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 5, 37–46
2023
2.
A. A. Magazev, I. V. Shirokov, “The structure of differential invariants for a free symmetry group action”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 6, 31–40
2016
3.
O. L. Kurnyavko, I. V. Shirokov, “Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods”, Theoret. and Math. Phys., 188:1 (2016), 965–979
2015
4.
M. M. Goncharovskiy, I. V. Shirokov, “Differential invariants and operators of invariant differentiation of the projectable action of Lie groups”, Theoret. and Math. Phys., 183:2 (2015), 619–636
5.
Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov, “Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras”, SIGMA, 11 (2015), 66–17
A. S. Popov, I. V. Shirokov, “Star product on the Lie coalgebra and its application for calculation of quantum integrals of motion”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(30) (2013), 379–386
7.
Breev, A.I., Goncharovskii, M.M., Shirokov, I.V., “Klein-Gordon equation with a special type of nonlocal nonlinearity in commutative homogeneous spaces with invariant metric”, Russian Physics Journal, 56:7 (2013), 10.1007/s11182-013-0092-7 , 8 pp.
2011
8.
A. I. Breev, I. V. Shirokov, A. A. Magazev, “Vacuum polarization of a scalar field on Lie groups and homogeneous spaces”, Theoret. and Math. Phys., 167:1 (2011), 468–483
9.
Goncharovskii, M.M., Shirokov, I.V., “Classification of degenerate solutions of linear differential equations”, Russian Physics Journal, 2011, no. 5, 10.1007/s11182-011-9649-5 , 8 pp.
2010
10.
I. V. Shirokov, “Symmetric cipher on the base of non-commutative algebra of polynomials”, Prikl. Diskr. Mat., 2010, no. supplement № 3, 35–36
2009
11.
I. V. Shirokov, A. V. Prolubnikov, “Algorithms for the graph isomorphism problem based on graph deregularisation”, Prikl. Diskr. Mat., 2009, no. supplement № 1, 101–102
12.
S. P. Baranovskii, I. V. Shirokov, “Deformations of vector fields and canonical coordinates on coadjoint orbits”, Siberian Math. J., 50:4 (2009), 580–586
13.
M. M. Goncharovskiy, I. V. Shirokov, “An integrable class of differential equations with nonlocal nonlinearity on Lie groups”, Theoret. and Math. Phys., 161:3 (2009), 1604–1615
2008
14.
O. L. Kurnyavko, I. V. Shirokov, “Construction of invariant scalar particle wave equations on Riemannian manifolds with external gauge fields”, Theoret. and Math. Phys., 156:2 (2008), 1169–1179
15.
A. A. Magazev, I. V. Shirokov, Yu. A. Yurevich, “Integrable magnetic geodesic flows on Lie groups”, Theoret. and Math. Phys., 156:2 (2008), 1127–1141
2007
16.
I. V. Shirokov, “Differential invariants of the transformation group of a homogeneous space”, Siberian Math. J., 48:6 (2007), 1127–1140
2006
17.
A. A. Magazev, I. V. Shirokov, “Hamiltonian systems in variations and the integration of the Jacobi equation on homogeneous spaces”, Russian Math. (Iz. VUZ), 50:8 (2006), 38–49
2003
18.
A. A. Magazev, I. V. Shirokov, “Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group”, Theoret. and Math. Phys., 136:3 (2003), 1212–1224
19.
S. P. Baranovskii, I. V. Shirokov, “Prolongations of Vector Fields on Lie Groups and Homogeneous Spaces”, Theoret. and Math. Phys., 135:1 (2003), 510–519
2001
20.
S. P. Baranovskii, V. V. Mikheyev, I. V. Shirokov, “Quantum Hamiltonian Systems on K-Orbits: Semiclassical Spectrum of the Asymmetric Top”, Theoret. and Math. Phys., 129:1 (2001), 1311–1319
21.
I. V. Shirokov, “Identities and Invariant Operators on Homogeneous Spaces”, Theoret. and Math. Phys., 126:3 (2001), 326–338
2000
22.
I. V. Shirokov, “Darboux coordinates on $K$-orbits and the spectra of Casimir operators on Lie groups”, Theoret. and Math. Phys., 123:3 (2000), 754–767
1999
23.
I. V. Shirokov, “Investigation of the stability of solutions of differential equations that admit a transitive symmetry group”, Russian Math. (Iz. VUZ), 43:3 (1999), 56–62
1996
24.
A. A. Drokin, A. V. Shapovalov, I. V. Shirokov, “Local symmetry algebra of Shrödinger equation for Hydrogen atom”, Theoret. and Math. Phys., 106:2 (1996), 227–236
25.
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration method for linear partial differential equations. Functional algebras and dimensional reduction”, Theoret. and Math. Phys., 106:1 (1996), 1–10
1995
26.
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, Theoret. and Math. Phys., 104:2 (1995), 921–934
1994
27.
Shirokov I.V., ALGEBRAIChESKIE PROBLEMY TEORII SIMMETRII I METODY INTEGRIROVANIYa POLEVYKh URAVNENII, Spetsialnost: 01.04.02 - Teoreticheskaya fizika, Izd-vo OmGTU, Tomsk, 1994
28.
Yugay, K.N., Blinov, N.V., Shirokov, I.V., “Asymptotic states in long Josephson junctions in an external magnetic field”, Physical Review B, 49:17 (1994), 12036-12039
A. V. Shapovalov, I. V. Shirokov, “Symmetry algebras of linear differential equations”, Theoret. and Math. Phys., 92:1 (1992), 697–703
1991
30.
V. G. Bagrov, A. V. Shapovalov, I. V. Shirokov, “Generation of new exactly solvable potentials of a nonstationary Schrödinger equation”, Theoret. and Math. Phys., 87:3 (1991), 635–640
1990
31.
V. G. Bagrov, B. F. Samsonov, A. V. Shapovalov, I. V. Shirokov, “Identities on solutions of the wave equation in the enveloping algebra of the conformal group”, Theoret. and Math. Phys., 83:1 (1990), 347–353