D. I. Borisov. Asimptotiki i otsenki sobstvennykh elementov Laplasiana s chastoi neperiodicheskoi smenoi granichnykh uslovii // Izvestiya RAN. Seriya matematicheskaya. 2003. T. 67. No. 6. C. 23-70
D. Borisov. Asymptotic behaviour of the spectrum of a waveguide with distant perturbation // Mathematical Physics, Analysis and Geometry. 2007. V. 10. No. 2. P. 155-196.
D.I. Borisov. O spektre dvumernogo periodicheskogo operatora s malym lokalizovannym vozmuscheniem // Izvestiya RAN. Seriya matematicheskaya. 2011. T. 75. # 3. S. 29-64.
D.I. Borisov, K.V. Pankrashkin. Otkrytie lakun i rasscheplenie kraev zon dlya volnovodov, soedinennykh periodicheskoi sistemoi malykh okon // Matematicheskie zametki. 2013. T. 93, # 5. S. 665-683.
D. Borisov. The spectrum of two quantum layers coupled by a window // Journal of Physics A: Mathematical and Theoretical. 2007. V. 40. No. 19. P. 5045-5066.
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for nonlocal one–dimensional Schroedinger operator with Neumann condition and translation in free term”, Lobachevskii Journal of Mathematics (to appear)
2.
D. I. Borisov, A. A. Fedotov, “On uniform asymptotics for resonances of Schrödinger operator on axis with fast decaying oscillating potential”, Mat. Sb. (to appear)
2026
3.
D. I. Borisov, I. A. Taimanov, “Examples of periodic Schrödinger operators with degenerate trace of the monodromy matrix”, Math. Notes, 120:6 (2026), 1148–1151 (to appear)
4.
Math. Notes, 120:2 (2026), 396–401
5.
D. I. Borisov, I. A. Taimanov, “On degeneration of hill discriminant for periodic Schrödinger operator”, Dokl. RAN. Math. Inf. Proc. Upr., 531 (2026), 80–87
6.
D. I. Borisov, E. A. Zhizhina, A. L. Piatnitski, “On exponentially small eigenvalues of small convolution operator with finite potential”, Dokl. RAN. Math. Inf. Proc. Upr., 531 (2026), 72–79
7.
Math. Notes, 120:5 (2026), 970–975 (to appear)
2025
8.
D. I. Borisov, R. R. Suleimanov, “Operator estimates for elliptic equations in multidimensional domains with strongly curved boundaries”, Sb. Math., 216:1 (2025), 25–53
9.
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina, “Non-local convolution type operators with potential: essential and infinite discrete spectrum”, Mathematical Methods in the Applied Sciences, 2025 (to appear)
10.
S. V. Dmitriev, D. Xiong, D. I. Borisov, M. G. Velarde, “The effect of nonlinearity on the efficiency of a thermal rectifier in the form of a junction of two chains”, The European Physical Journal Special Topics, 2025 (to appear)
11.
D. I. Borisov, D. M. Polyakov, “Spectral asymptotics for Schrödinger operator perturbed by translation operator”, Izv. Math., 89:3 (2025), 442–460
12.
D. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic equations in two-dimensional domains with fast oscillating boundary and frequent alternation of boundary conditions”, Sb. Math., 216:8 (2025), 1037–1054
13.
Denis Borisov, Elena Zhizhina, Andrey Piatnitski, “On infinite discrete spectrum of convolution operators with potentials”, Funct. Anal. Appl., 59:4 (2025), 457–461
14.
D. I. Borisov, A. L. Piatnitski, “Orlicz type spaces related with nonlinear nonlocal functionals”, Dokl. RAN. Math. Inf. Proc. Upr., 526 (2025), 8–15
15.
D. I. Borisov, A. R. Danilin, V. Yu. Novokshenov, “Tribute to Arlen Mikhailovich Il'in”, Sb. Math., 216:8 (2025), 1019–1020
2024
16.
D. I. Borisov, “Operator estimates for non-periodically perforated domains: disappearance of cavities”, Applicable Analysis, 103:5 (2024), 859–873
D. I. Borisov, D. A. Zezyulin, “On perturbation of thresholds in essential spectrum under the coincidence of virtual level and spectral singularity”, Russian Journal of Mathematical Physics, 31:1 (2024), 321–341
18.
D. I. Borisov, R. R. Suleimanov, “On operator estimates for elliptic operators with mixed boundary conditions in two-dimensional domains with rapidly oscillating boundary”, Math. Notes, 116:2 (2024), 182–199
19.
D. I. Borisov, “Geometric approximation of point interactions in three-dimensional domains”, Mathematics, 12:7 (2024), 1031, 26 pp.
D.I. Borisov, R.R. Suleimanov, “Operator estimates for problems in domains with singular curved boundary: Dirichlet and Neumann conditions”, Doklady Mathematics, 109:1 (2024), 6–11
21.
D.I. Borisov, R.R. Suleimanov, “Operator estimates for problems in domains with singular curved boundary: Dirichlet and Neumann conditions”, Doklady Mathematics, 109:1 (2024), 6–11
22.
D. I. Borisov, D. M. Polyakov, “Uniform spectral asymptotics for Schroedinger operator on segment with delta-interaction”, Russian Journal of Mathematical Physics, 31:2 (2024), 149–161
D. I. Borisov, A. A. Fedotov., “On the point spectrum of a non-self-adjoint quasiperiodic operator”, Russian Journal of Mathematical Physics, 31:3 (2024), 389–406
D. I. Borisov, D. M. Polyakov, “Asymptotics for eigenvalues of Schroedinger operator with small translation and Dirichlet condition”, Doklady Mathematics, 109:3 (2024), 227–231
25.
D. I. Borisov, D. M. Polyakov, “Uniform asymptotics for eigenvalues of model Schrödinger operator with small translation”, Ufa Math. J., 16:3 (2024), 1–20
26.
D. I. Borisov, “Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term”, Mathematical Methods in the Applied Sciences, 47:6 (2024), 4122–4164, arXiv: 2205.09490
D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential-difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260, 34 pp.
D. I. Borisov, “Homogenization of Operators with Perturbations of General Form in the Lower-Order Terms”, Math. Notes, 113:1 (2023), 139–143
29.
D. I. Borisov, J. Kříž, “Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit”, Analysis and Mathematical Physics, 13 (2023), 5, 34 pp.
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina., “On spectra of convolution operators with potentials”, Journal of Mathematical Analysis and Applications, 517:1 (2023), 126568, 27 pp.
D. I. Borisov, D. A. Zezyulin, “On bifurcations of thresholds in essential spectrum under presence of spectral singularity”, Differential Equations, 59:2 (2023), 278–282https://doi.org/10.1134/S0012266123020118
32.
D. I. Borisov, “Geometric approximation of point interactions in two-dimensional domains for non-self-adjoint operators”, Mathematics, 11:4 (2023), 947, 23 pp. https://doi.org/10.3390/math11040947
D. I. Borisov, “Operator estimates in two-dimensional problems with a frequent alternation in the case of small parts with the Dirichlet condition”, Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S33–S52
34.
D. I. Borisov, P. Exner, “Approximation of point interactions by geometric perturbations in two-dimensional domains”, Bulletin of Mathematical Sciences, 13:2 (2023), 2250003, 30 pp.
D. I. Borisov, “Homogenization for operators with arbitrary perturbations of coefficients”, Journal of Differential Equations, 369 (2023), 41–93, arXiv: abs/2205.09490
D. I. Borisov, “On resolvent of the Schrödinger operator on a model graph with small loops”, Journal of Mathematical Sciences, 276:1 (2023), 48–60
37.
D. I. Borisov, D. A. Zezyulin, “Eigenvalues bifurcating from continuum in two-dimensional potentials generating non-Hermitian gauge fields”, Annals of Physics, 459 (2023), 169498, 17 pp.
G. Berkolaiko, D. I. Borisov, M. King, “Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge”, Analysis and Mathematical Physics, 13 (2023), 90, 22 pp.
39.
D. I. Borisov, A. L. Piatnitski and E. A. Zhizhina, “Spectrum of one-dimensional potential perturbed by a small convolution operator: general structure”, Mathematics, 11:19 (2023), 4042, 26 pp.
D. I. Borisov, A. A. Fedotov, “Monodromization and a PT-symmetric nonself-adjoint quasi-periodic operator”, Russian Journal of Mathematical Physics, 30:3 (2023), 294–309
D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence for problems with perforation alogn a given manifold and with a nonlinear Robin condition on the boundaries of cavities”, St. Petersburg Math. J., 35:4 (2024), 611–652
2023
42.
D. I. Borisov, D. M. Polyakov, “Resolvent convergence for differential-difference operators with small variable translations”, Mathematics, 11:20 (2023), 4260, 33 pp.
D. I. Borisov, A. L. Piatnitski, E. A. Zhizhina, “Spectrum of one-dimensional potential perturbed by a small convolution operator: general structure”, Mathematics, 11:19 (2023), 4042, 26 pp.
D. Borisov, “Resolvents of elliptic operators on quantum graphs with small edges: holomorphy and Taylor series”, Advances in Mathematics, 397 (2022), 108125, 48 pp., arXiv: 2102.12958
D. I. Borisov, L. I. Gazizova, “Taylor series for resolvents of operators on graphs with small edges”, Proceedings of Steklov Institute of Mathematics, 317:Suppl. 1 (2022), S37–S54
46.
D. I. Borisov, A. I. Mukhametrakhimova, “Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities”, Sb. Math., 213:10 (2022), 1318–1371
47.
D. I. Borisov, E. A. Zhizhina, A. L. Piatnitski, “Spectrum of a convolution operator with potential”, Russian Math. Surveys, 77:3 (2022), 546–548
48.
D. I. Borisov, A. A. Fedotov, “On Bloch solutions of difference equations”, Funct. Anal. Appl., 56:4 (2022), 239–250
49.
D. I. Borisov, “Asymptotic expansion of solution to Dirichlet problem in perforated domain: strange term case”, Ufa Mathematical Journal, 14:4 (2022), 26–41
50.
S. V. Dmitriev, D. I. Borisov, “Effective interatomic potential for modelling shock waves in carbon nanotube bundles”, AIP Conference Proceedings, 2533 (2022), 02005, 5 pp.
51.
D. I. Borisov, M. N. Konyrkulzhaeva, “Operator $L_2$-estimates for two-dimensional problems with frequent alternation of boundary conditions”, Journal of Mathematical Sciences, 267:3 (2022), 319–337
52.
D. I. Borisov, “Operator estimates for planar domains with irregularly curved boundary. The Dirichlet and Neumann conditions”, Journal of Mathematical Sciences, 264:5 (2022), 562–580
53.
D. I. Borisov,M. Znojil, “Arnold’s potentials and quantum catastrophes II”, Annals of Physics, 442 (2022), 168896, 15 pp.
D. I. Borisov, D. A. Zezyulin, “Bifurcations of essential spectra generated by a small non-Hermitian small hole. II. Eigenvalues and resonances”, Russian Journal of Mathematical Physics, 29:3 (2022), 321–341
D. I. Borisov, “Norm resolvent convergence of elliptic operators in domains with thin spikes”, Journal of Mathematical Sciences, 261:3 (2022), 366–391
2021
56.
D. I. Borisov, A. M. Golovina, “On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders”, Journal of Mathematical Analysis and Applications, 496:2 (2021), 124809, arXiv: 2008.07289
D. I. Borisov, G. Cardone, G. A. Chechkin, Yu. O. Koroleva, “On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary”, Calculus of Variations and Partial Differential Equations, 60:1 (2021), 48
D. I. Borisov, M. Täufer, I. Veseli{\c}, “Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum”, Journal of Statistical Physics, 182:1 (2021), 1
D. I. Borisov, P. Exner, “Gap opening in two-dimensional periodic systems”, Communications in Contemporary Mathematics, 23:1 (2021), 1950080, arXiv: 1810.08824
D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition”, Sb. Math., 212:8 (2021), 1068–1121
61.
D. I. Borisov, “Asymptotic analysis of boundary-value problems for the Laplace operator with frequently alternating type of boundary conditions”, Partial Differential Equations, CMFD, 67, no. 1, PFUR, M., 2021, 14–129
62.
D. I. Borisov, D. A. Zezyulin, M. Znojil, “Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations”, Studies in Applied Mathematics, 146:4 (2021), 834-880
D. I. Borisov, D. A. Zezyulin, “Bifurcations of essential spectra generated by a small non-Hermitian hole. I. Meromorphic continuations”, Russian Journal of Mathematical Physics, 28:4 (2021), 416–433
D. I. Borisov, M. N. Konyrkulzhaeva, A. I. Mukhametrakhimova, “On discrete spectrum of a model graph with loop and small edges”, Journal of Mathematical Sciences, 257:5 (2021), 3–18
2020
68.
D.I. Borisov, D.A. Zezyulin, “Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials”, Applied Mathematics Letters, 100 (2020), id 106049, arXiv: 1908.06384
D. I. Borisov, A. M. Golovina, A. I. Mukhametrakhimova, “Analytic continuation of resolvent of analytic continuation in cylinder”, Journal of Mathematical Sciences, 250:2 (2020), 260-284
70.
D. I. Borisov, G. Cardone, “On a one-dimensional quadratic operator pencil with a small periodic perturbation”, ESAIM: Control, Optimisation and Calculus of Variations, 26 (2020), 21, 32 pp.
M. Znojil, D. I. Borisov, “Anomalous mechanisms of the loss of observability in non-Hermitian quantum models”, Nuclear Physics B, 957 (2020), 115064, 19 pp.
D. I. Borisov, O.A. Sultanov, “Complete asymptotics for solution of singularly perturbed dynamical systems with single well potential”, Mathematics, 8:6 (2020), 949, 17 pp.
D. I. Borisov, A. I. Mukhametrakhimova, “On a model graph with a loop and small edges”, Journal of Mathematical Sciences, 251:5 (2020), 573-601
74.
D. I. Borisov, M. N. Konyrkulzhaeva, “On infinite system of resonance and eigenvalues with exponential asymptotics generated by distant perturbations”, Ufa Math. J., 12:4 (2020), 3–18
75.
A. M. Bayazitov, E. A. Korznikova, A. S. Semenov, D. I. Borisov and S. V. Dmitriev, “Interaction of supersonic 2-crowdions in fcc platinum”, IOP Conference Series: Materials Science and Engineering, 1008 (2020), 012068
I. R. Sunagatova, A. M. Subkhangulova, M. N. Semenova, A. S. Semenov, D. I. Borisov and S. V. Dmitriev, “Properties of one-dimensional nonlinear vibrational modes in triangular lattice with Lennard-Jones interactions”, IOP Conference Series: Materials Science and Engineering, 1008 (2020), 012073
D. I. Borisov, “On lacunas in the spectrum of the Laplacian with the Dirichlet boundary condition in a strip with oscillating boundary”, J. Math. Sci. (N. Y.), 257:3 (2021), 273–285
2019
78.
D. I. Borisov, M. N. Konyrkulzhaeva, “Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum”, Ufa Math. J., 11:2 (2019), 56–70
79.
D. I. Borisov, M. N. Konyrkulzhayeva, “Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge”, Journal of Mathematical Sciences, 239:3 (2019), 248-267
80.
D. I. Borisov, D. A. Zezyulin, “Spacing gain and absorption in a simple PT-symmetric model: spectral singularities and ladders of eigenvalues and resonances”, Journal of Physics A, 52:44 (2019), id 445202, arXiv: 1908.06383
D. I. Borisov, “Bethe-Sommerfeld conjecture for periodic Schroedinger operators in strip”, Journal of Mathematical Analysis and Applications, 479:1 (2019), 260–282, arXiv: 1806.09292
D. I. Borisov, A. M. Golovina, “On occurrence of resonances from multiple eigenvalues of the Schrödinger operator in a cylinder with scattering perturbations”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 3–14
2020
83.
D.I. Borisov, “On elliptic operators with frequent alternation of boundary conditions along a given curve”, Journal of Mathematical Sciences, 244:3 (2020), 378-389
2018
84.
D.I. Borisov, “Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip”, Theoret. and Math. Phys., 195:2 (2018), 690–703
85.
D. Borisov, F. Hoecker-Escuti, I. Veselic, “Expansion of the spectrum in the weak disorder regime for random operators in continuum space”, Communications in Contemporary Mathematics, 20:1 (2018), id 1750008
D. Saadatmand, D.I. Borisov, P.G. Kevrekidis, K. Zhou, S.V. Dmitriev, “Resonant interaction of φ4 kink with spatially periodic PT-symmetric perturbation with spatially periodic gain/loss coefficient”, Communications in Nonlinear Science and Numerical Simulation, 56 (2018), 62-76
D.I. Borisov, A.I. Mukhametrakhimova, “On norm resolvent convergence for elliptic operators in multi-dimensional domains with small holes”, Journal of Mathematical Sciences, 2018, no. 3, 283-298
2019
88.
D. I. Borisov, “Gaps in the spectrum of the Laplacian in a band with periodic delta interaction”, Proc. Steklov Inst. Math. (Suppl.), 305, suppl. 1 (2019), S16–S23
2018
89.
M. Znojil, D. Borisov, “Two patterns of PT-symmetry breakdown in a non-numerical six-state simulation”, Annals of Physics, 394 (2018), 40-49
D.I. Borisov, M. Täufer, I. Veselić, “Spectral localization for quantum Hamiltonians with weak random delta interaction”, Comptes Rendus Mathématique, 356:6 (2018), 686-691
D. I. Borisov, “On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation”, Ufa Math. Journal, 10:2 (2018), 14–30
2021
92.
D. I. Borisov, “Perturbations of the Continuous Spectrum of a Certain Nonlinear Two-Dimensional Operator Sheaf”, J. Math. Sci. (N. Y.), 252:2 (2021), 135–146
2017
93.
D. Borisov, M. Tautenhahn, I. Veselic, “Scale-free quantitative unique continuation and equidistribution estimates for solutions of elliptic differential equations”, Journal of Mathematical Physics, 58:12 (2017), id 121502, arXiv: 1512.06347
D. I. Borisov, S. V. Dmitriev, “On the spectral stability of kinks in 2D Klein-Gordon model with parity-time-symmetric perturbation”, Studies in Applied Mathematics, 138:3 (2017), 317-342, arXiv: 1512.01103
D. Borisov, P. Freitas, “The spectrum of geodesic balls on spherically symmetric manifolds”, Communications in Analysis and Geometry, 25:3 (2017), 507-544, arXiv: 1603.02399
D. I. Borisov, M. Znojil, “On eigenvalues of a $\mathscr{P\!T}$-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199
2019
97.
D.I. Borisov, “Estimates of initial scales for layers with small random negative-definite perturbations”, Journal of Mathematical Sciences, 241:5 (2019), 518–548
2017
98.
D.I. Borisov, “Initial length scale estimate for the Schroedginer operator with a random fast oscillating potential in a multi-dimensional layer”, Vestnik Kazakhskogo natsionalnogo universiteta. Seriya matematika, mekhanika, informatika., 93:1 (2017), 21-31
99.
D. I. Borisov, “On lacunas in the lower part of the spectrum of the periodic magnetic operator in a strip”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 373–391
2016
100.
D. Borisov, G. Cardone, T. Durante, “Homogenization and norm resolvent convergence for elliptic operators in a strip perforated along a curve”, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 146:6 (2016), 1115–1158, arXiv: 1305.1009
D. Borisov, F. Hoecker-Escuti, I. Veselić, “Expansion of the almost sure spectrum in the weak disorder regime”, Journal of Functional Analysis, 270:5 (2016), 1684–1718 , Academic Press
D. I. Borisov, “Creation of spectral bands for a periodic domain with small windows”, Russian Journal of Mathematical Physics, 23:1 (2016), 19–34 , Pleiades Publishing
D. I. Borisov, T. F. Sharapov, “On the Resolvent of Multidimensional Operators with Frequently Alternating Boundary Conditions with the Robin Homogenized Condition”, Journal of Mathematical Sciences, 213:4 (2016), 461–503 , Springer US ; D. I. Borisov, T. F. Sharapov, “O rezolvente mnogomernykh operatorov s chastoi smenoi kraevykh uslovii v sluchae tretego usrednennogo usloviya”, Problemy matematicheskogo analiza, 83 (2015), 3-40
D. I. Borisov, M. Znojil, “Mathematical and Physical Meaning of the Crossings of Energy Levels in PT-Symmetric Systems”, Non-Hermitian Hamiltonians in Quantum Physics, Springer International Publishing, 2016, 201–217
D. Borisov, A. Golovina, I. Veselić, “Quantum Hamiltonians with weak random abstract perturbation. I. Initial length scale estimate”, Annales Henri Poincare, 17:9 (2016), 2341-2377
D.I. Borisov, R. Kh. Karimov, T. F. Sharapov, “Initial length scale estimate for waveguides with some random singular potentials”, Ufa Math. Journal, 7:2 (2015), 33–54
108.
JETP Letters, 101:7 (2015), 497–502
109.
D.I. Borisov, “The Emergence of Eigenvalues of a $\mathcal{PT}$-Symmetric Operator in a Thin Strip”, Math. Notes, 98:6 (2015), 872–883
110.
D. I. Borisov, “On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows”, Russian Journal of Mathematical Physics, 22:2 (2015), 153–160 , Pleiades Publishing
D. Borisov, I. Nakić, Ch. Rose, M. Tautenhahn, I. Veselić, “Multiscale unique continuation properties of eigenfunctions”, Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, Springer International Publishing, 2015, 107–118
112.
D. I. Borisov, F. Ružička, M. Znojil, “Multiply degenerate exceptional points and quantum phase transitions”, International Journal of Theoretical Physics, 54:12 (2015), 4293–4305 , Springer US
D. I. Borisov, “Perturbation of threshold of essential spectrum for waveguides with windows. I: Decreasing resonance solutions”, Journal of Mathematical Sciences, 205:2 (2015), 141–181 , Springer US
D. Saadatmand, S. V. Dmitriev, D. I. Borisov, P. G. Kevrekidis, M. A. Fatykhov, K. Javidan, “Kink scattering from a parity-time-symmetric defect in the $\phi$ 4 model”, Communications in Nonlinear Science and Numerical Simulation, 29:1 (2015), 267–282 , Elsevier
D. I. Borisov, “Perturbation of Threshold of Essential Spectrum for Waveguides with Windows. II: Asymptotics”, Journal of Mathematical Sciences, 210:5 (2015), 590–621 , Springer US
D. Borisov, M. Tautenhahn, I. Veselic, “Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators”, Mathematical Results in Quantum Mechanics, 2014, 89–99
D. Borisov, G. Cardone, T. Durante, “Norm-resolvent convergence for elliptic operators in domain with perforation along curve”, Comptes Rendus Mathematique, 352:9 (2014), 679–683 , Elsevier Masson
D. Saadatmand, S. V. Dmitriev, D. I. Borisov, P. G. Kevrekidis, “Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect”, Physical Review E, 90:5 (2014), 052902 , American Physical Society
S. V. Suchkov, D. I. Borisov, A. A. Sukhorukov, Yu. S. Kivshar, others, “Signal manipulation with a PT-symmetric coupler embedded into an array of optical waveguides”, Pisma o materialakh, 4:4 (2014), 222–225
2013
122.
D. I. Borisov, K. V. Pankrashin, “Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows”, Math. Notes, 93:5 (2013), 660–675
123.
D.I. Borisov, K. V. Pankrashin, “On the Extrema of Band Functions in Periodic Waveguides”, Funct. Anal. Appl., 47:3 (2013), 238–240
124.
D. Borisov, R. Bunoiu, G. Cardone, “Waveguide with non-periodically alternating Dirichlet and Robin conditions: homogenization and asymptotics”, Zeitschrift für angewandte Mathematik und Physik, 64:3 (2013), 439–472 , SP Birkhäuser Verlag Basel
D. Borisov, K. Pankrashkin, “Quantum waveguides with small periodic perturbations: gaps and edges of Brillouin zones”, Journal of Physics A: Mathematical and Theoretical, 46:23 (2013), 235203 , IOP Publishing
2026
