asymptotic techniques; pseudodifferential operators with discontinuous symbols; singular integral equations; nonlinear equations of mathematical physics; spectral theory.
Main publications:
Budylin A. M., Buslaev V. S. Reflection operators and their applications to asymptotic investigations of semiclassical integral equations // Adv. Soviet Math. V. 7. Providence, RI: AMS, 1991, 107–157.
Budylin A. M., Buslaev V. S. Semiclassical asymptotics of the resolvent of the integral convolution operator with the sine-kernel on a finite interval // St. Petersburg Math. J., 1996, 7(6), 925–942.
Budylin A. M., Buslaev V. S. The Gelfand–Levitan–Marchenko equation and the long-time asymptotics of solutions of the nonlinear Schr{\"o}dinger equation // St. Petersburg Math. J., 2001, 12(5).
A. M. Budylin, S. B. Levin, T. S. Yurova, “Asymptotics of the solution of the Dirichlet problem for the Laplace equation in a strip with thin branches”, Mat. Zametki, 116:3 (2024), 355–371; Math. Notes, 116:3 (2024), 432–445
2023
2.
A. M. Budylin, S. B. Levin, “Solution of the Quantum Three-Body Problem in a Neighborhood of Three-Particle Forward Scattering Direction”, Mat. Zametki, 113:3 (2023), 332–346; Math. Notes, 113:3 (2023), 327–338
3.
A. M. Budylin, S. B. Levin, “On the main term of the asymptotics of the problem of few charged particles in the presence of bound states”, Zap. Nauchn. Sem. POMI, 521 (2023), 59–78
2020
4.
A. M. Budylin, “Singular matrix factorization problem with quadratically oscillating off-diagonal elements. Quasiclassical asymptotics of solutions with a diagonal element vanishing at the stationary point”, Algebra i Analiz, 32:5 (2020), 37–61; St. Petersburg Math. J., 32:5 (2021), 847–864
5.
A. M. Budylin, S. B. Levin, “The scattering problem of three one-dimensional quantum particles. The case of pair Coulomb potentials of repulsion at large distances”, Zap. Nauchn. Sem. POMI, 493 (2020), 88–101
I. V. Baibulov, A. M. Budylin, S. B. Levin, “The scattering problem of three one-dimensional short-range quantum particles involving bound states in pair subsystems. The coordinate asymptotics of the resolvent kernel and absolutely continuous spectrum eigenfunctions”, Zap. Nauchn. Sem. POMI, 483 (2019), 5–18
I. V. Baibulov, A. M. Budylin, S. B. Levin, “The absolutely continuous spectrum eigenfunctions asymptotics of the three one-dimensional quantum particles scattering problem”, Zap. Nauchn. Sem. POMI, 471 (2018), 15–37; J. Math. Sci. (N. Y.), 243:5 (2019), 640–655
A. M. Budylin, Ya. U. Koptelov, S. B. Levin, “Some aspects of the scattering problem for the system of three charged particles”, Zap. Nauchn. Sem. POMI, 461 (2017), 65–94; J. Math. Sci. (N. Y.), 238:5 (2019), 601–620
I. V. Baybulov, A. M. Budylin, S. B. Levin, “Few one-dimensional quantum particles scattering problem. The structure and asymptotics of the resolvent kernel limit values”, Zap. Nauchn. Sem. POMI, 461 (2017), 14–51; J. Math. Sci. (N. Y.), 238:5 (2019), 566–590
A. M. Budylin, S. V. Sokolov, “Convolution equations on expanding interval with symbols having zeros or poles of nonintegral power”, Zap. Nauchn. Sem. POMI, 451 (2016), 29–42; J. Math. Sci. (N. Y.), 226:6 (2017), 711–719
2015
11.
A. M. Budylin, S. B. Levin, “To the question of Schröedinger operator kernel resolvent asymptotics construction in the three one-dimensional quantum particles scattering problem interacting by finite repulsive pair potentials”, Zap. Nauchn. Sem. POMI, 438 (2015), 95–103; J. Math. Sci. (N. Y.), 224:1 (2017), 63–68
A. M. Budylin, S. B. Levin, “The equation of convolution on a large finite interval with the symbol which has zeros of nonintegral powers”, Zap. Nauchn. Sem. POMI, 438 (2015), 83–94; J. Math. Sci. (N. Y.), 224:1 (2017), 54–62
A. M. Budylin, V. S. Buslaev, “Quasi-Classical Asymptotics of Solutions to the Matrix Factorization Problem with Quadratically Oscillating Off-Diagonal Elements”, Funktsional. Anal. i Prilozhen., 48:1 (2014), 1–18; Funct. Anal. Appl., 47:1 (2014), 1–14
A. M. Budylin, “Semiclassical asymptotics of the solutions of matrix Riemann–Hilbert problems with fast oscillation of non-diagonal elements”, Algebra i Analiz, 25:2 (2013), 75–100; St. Petersburg Math. J., 25:2 (2014), 205–222
15.
V. M. Babich, A. M. Budylin, L. A. Dmitrieva, A. I. Komech, S. B. Levin, M. V. Perel', E. A. Rybakina, V. V. Sukhanov, A. A. Fedotov, “On the mathematical work of Vladimir Savel'evich Buslaev”, Algebra i Analiz, 25:2 (2013), 3–36; St. Petersburg Math. J., 25:2 (2014), 151–174
2000
16.
A. M. Budylin, V. S. Buslaev, “The Gel'fand–Levitan–Marchenko equation and the asymptotic behavior of solutions of the nonlinear Schrödinger equation for large time values”, Algebra i Analiz, 12:5 (2000), 64–105; St. Petersburg Math. J., 12:5 (2001), 761–789
A. M. Budylin, V. S. Buslaev, “Quasiclassical integral equations and the asymptotic behavior of
solutions of the Korteweg–de Vries equation for large time values”, Dokl. Akad. Nauk, 348:4 (1996), 455–458
A. M. Budylin, V. S. Buslaev, “Quasiclassical asymptotics of the resolvent of an integral convolution operator with a sine kernel on a finite interval”, Algebra i Analiz, 7:6 (1995), 79–103; St. Petersburg Math. J., 7:6 (1996), 925–942
A. M. Budylin, V. S. Buslaev, “Quasiclassical integral equations with slowly decreasing kernels on bounded domains”, Algebra i Analiz, 5:1 (1993), 160–178; St. Petersburg Math. J., 5:1 (1994), 141–158
A. M. Budylin, V. S. Buslaev, “Asymptotic behavior of spectral characteristics of an integral
operator with difference kernel on expanding domains”, Dokl. Akad. Nauk SSSR, 287:3 (1986), 529–532
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