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
A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, Theoret. and Math. Phys., 104:2 (1995), 921–934
2.
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
3.
A. V. Shapovalov, I. V. Shirokov, “Symmetry algebras of linear differential equations”, Theoret. and Math. Phys., 92:1 (1992), 697–703
4.
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
5.
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
6.
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
7.
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
8.
I. V. Shirokov, “Identities and Invariant Operators on Homogeneous Spaces”, Theoret. and Math. Phys., 126:3 (2001), 326–338
9.
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
10.
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. 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
12.
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
13.
I. V. Shirokov, “Differential invariants of the transformation group of a homogeneous space”, Siberian Math. J., 48:6 (2007), 1127–1140
14.
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
S. P. Baranovskii, I. V. Shirokov, “Deformations of vector fields and canonical coordinates on coadjoint orbits”, Siberian Math. J., 50:4 (2009), 580–586
16.
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
17.
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
18.
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
19.
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.
20.
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
21.
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
22.
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
23.
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
24.
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.
25.
I. V. Shirokov, “Symmetric cipher on the base of non-commutative algebra of polynomials”, Prikl. Diskr. Mat., 2010, no. supplement № 3, 35–36
26.
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
27.
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
28.
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
29.
Shirokov I.V., ALGEBRAIChESKIE PROBLEMY TEORII SIMMETRII I METODY INTEGRIROVANIYa POLEVYKh URAVNENII, Spetsialnost: 01.04.02 - Teoreticheskaya fizika, Izd-vo OmGTU, Tomsk, 1994
30.
O. L. Kurnyavko, I. V. Shirokov, “Construction of first-order invariant differential operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 5, 37–46
31.
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