Boundray problems to Maxwell Equations, Spectel problems of waveguide theory, Embedding theorems for vector functional spaces, mixed finite elements.
Main publications:
Delitsyn A. L. O postanovke kraevykh zadach dlya sistemy uravnenii Maksvella v tsilindre i ikh razreshimosti // Izvestiya RAN. Seriya matematicheskaya. 2007. T. 71. # 3. S. 61–112.
Delitsyn A. L. Zadacha difraktsii elektromagnitnogo polya v svobodnom prostranstve // Differentsialnye uravneniya. 2005. T. 41. # 8. S. 1–7.
Delitsyn A. L. Zadacha difraktsii v volnovode // Differentsialnye uravneniya. 2005. T. 41. # 3. S. 393–400.
Delitsyn A. L. Zadacha difraktsii elektromagnitnogo polya v tsilindricheskoi oblasti // Doklady RAN. 2004. T. 398. # 3. C. 310–313.
Delitsyn A. L. O diskretnom spektre operatora Laplasa v tsilindre s lokalno vozmuschennoi granitsei // Differentsialnye uravneniya. 2004. T. 40. # 2. S. 198–207.
A. L. Delitsyn, “Fast Algorithms for Solving the Inverse Scattering Problem
for the Zakharov–Shabat System of Equations
and Their Applications”, Mat. Zametki, 112:2 (2022), 198–217; Math. Notes, 112:2 (2022), 199–214
A. L. Delitsyn, “Localization of eigenfunctions of the Laplace operator in a domain with a perforated barrier”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 984–989; Comput. Math. Math. Phys., 59:6 (2019), 936–941
A. L. Delitsyn, L. L. Delitsyn, “On a nonlinear spectral problem for a dielectric waveguide with Kerr nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 59:5 (2019), 762–774; Comput. Math. Math. Phys., 59:5 (2019), 718–730
2018
4.
A. L. Delitsyn, “On the dispersion curves of anisotropic waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1189–1196; Comput. Math. Math. Phys., 58:7 (2018), 1142–1149
A. L. Delitsyn, “On the character of increase in the field upon resonance excitation of a waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 56:12 (2016), 2086–2091; Comput. Math. Math. Phys., 56:12 (2016), 2056–2061
D. A. Konyaev, A. L. Delitsyn, “Finite element method with partial radiation conditions for diffraction problem on domains of complex structure”, Matem. Mod., 26:8 (2014), 48–64
A. L. Delitsyn, “Remark on resonance scattering by two barriers in a waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 52:7 (2012), 1289–1293; Comput. Math. Math. Phys., 52:7 (2012), 1055–1059
2011
8.
A. L. Delitsyn, “On the completeness of the system of eigenvectors of electromagnetic waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 51:10 (2011), 1883–1888; Comput. Math. Math. Phys., 51:10 (2011), 1771–1776
A. L. Delitsyn, “Finite element method for the diffraction problem in a waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010), 1926–1930; Comput. Math. Math. Phys., 50:11 (2010), 1825–1829
2009
10.
A. L. Delitsyn, “Partial radiation conditions and hypersingular integral operators”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1652–1658; Comput. Math. Math. Phys., 49:9 (2009), 1576–1582
A. L. Delitsyn, “The statement and solubility of boundary-value problems
for Maxwell's equations in a cylinder”, Izv. RAN. Ser. Mat., 71:3 (2007), 61–112; Izv. Math., 71:3 (2007), 495–544
A. L. Delitsyn, “A Diffraction Problem for Electromagnetic Field in Free Space”, Differ. Uravn., 41:7 (2005), 881–888; Differ. Equ., 41:7 (2005), 923–931
13.
A. L. Delitsyn, “A Diffraction Problem in a Waveguide”, Differ. Uravn., 41:3 (2005), 375–381; Differ. Equ., 41:3 (2005), 393–400
2004
14.
A. L. Delitsyn, “The Discrete Spectrum of the Laplace Operator in a Cylinder with Locally Perturbed Boundary”, Differ. Uravn., 40:2 (2004), 198–207; Differ. Equ., 40:2 (2004), 207–217
A. N. Bogolyubov, A. L. Delitsyn, M. D. Malykh, “On an example of trapped modes in an irregular waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 43:1 (2003), 127–132; Comput. Math. Math. Phys., 43:1 (2003), 124–129
A. N. Bogolyubov, A. L. Delitsyn, M. D. Malykh, “On the root vectors of a cylindrical waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 41:1 (2001), 126–129; Comput. Math. Math. Phys., 41:1 (2001), 121–124
A. L. Delitsyn, “An approach to the completeness of normal waves in a waveguide with magnetodielectric filling”, Differ. Uravn., 36:5 (2000), 629–633; Differ. Equ., 36:5 (2000), 695–700
A. L. Delitsyn, “On the problem of scattering in a nonuniform waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 40:4 (2000), 606–610; Comput. Math. Math. Phys., 40:4 (2000), 577–581
A. N. Bogolyubov, A. L. Delitsyn, A. G. Sveshnikov, “On the problem of excitation of a waveguide filled with an inhomogeneous medium”, Zh. Vychisl. Mat. Mat. Fiz., 39:11 (1999), 1869–1888; Comput. Math. Math. Phys., 39:11 (1999), 1794–1813
A. L. Delitsyn, “Application of the finite element method to the calculation of modes of dielectric waveguides”, Zh. Vychisl. Mat. Mat. Fiz., 39:2 (1999), 315–322; Comput. Math. Math. Phys., 39:2 (1999), 298–304
A. N. Bogolyubov, A. L. Delitsyn, A. G. Sveshnikov, “On the completeness of the set of eigen- and associated functions of a waveguide”, Zh. Vychisl. Mat. Mat. Fiz., 38:11 (1998), 1891–1899; Comput. Math. Math. Phys., 38:11 (1998), 1815–1823
V. F. Butuzov, A. A. Bykov, A. L. Delitsyn, M. K. Kerimov, I. E. Mogilevskii, Yu. V. Mukhartova, N. N. Nefedov, A. G. Sveshnikov, D. D. Sokoloff, N. A. Tikhonov, N. E. Shapkina, A. G. Yagola, “On the 70th anniversary of birthday of Professor Aleksandr Nikolaevich Bogolyubov”, Zh. Vychisl. Mat. Mat. Fiz., 55:10 (2015), 1635–1636
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