Chernyshev, V. L.; Nazaikinskii, V. E.; Tsvetkova, A. V. Lattice equations and semiclassical asymptotics. (English) Zbl 1528.81142 Russ. J. Math. Phys. 30, No. 2, 152-164 (2023). MSC: 81Q20 58J37 81R30 14M17 05C05 81Q30 PDFBibTeX XMLCite \textit{V. L. Chernyshev} et al., Russ. J. Math. Phys. 30, No. 2, 152--164 (2023; Zbl 1528.81142) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides. (English. Russian original) Zbl 1519.35061 Theor. Math. Phys. 214, No. 1, 1-23 (2023); translation from Teor. Mat. Fiz. 214, No. 1, 3-29 (2023). MSC: 35C20 35S05 53D12 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 214, No. 1, 1--23 (2023; Zbl 1519.35061); translation from Teor. Mat. Fiz. 214, No. 1, 3--29 (2023) Full Text: DOI
Chernyshev, V. L.; Hilberdink, T. W.; Minenkov, D. S.; Nazaikinskii, V. E. Restricted partitions: the polynomial case. (English. Russian original) Zbl 1520.11085 Funct. Anal. Appl. 56, No. 4, 299-309 (2022); translation from Funkts. Anal. Prilozh. 56, No 4, 80-92 (2022). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N37 11B75 05C80 PDFBibTeX XMLCite \textit{V. L. Chernyshev} et al., Funct. Anal. Appl. 56, No. 4, 299--309 (2022; Zbl 1520.11085); translation from Funkts. Anal. Prilozh. 56, No 4, 80--92 (2022) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Homogenization of the Cauchy problem for the wave equation with rapidly varying coefficients and initial conditions. (English) Zbl 1501.35031 Manuilov, Vladimir M. (ed.) et al., Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6–9, 2018. Cham: Birkhäuser. Trends Math., 77-102 (2021). MSC: 35B27 35L05 35L15 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, in: Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6--9, 2018. Cham: Birkhäuser. 77--102 (2021; Zbl 1501.35031) Full Text: DOI
Dobrokhotov, Sergey Yu.; Nazaikinskii, Vladimir E.; Shafarevich, Andrei I. Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. (English. Russian original) Zbl 1492.81056 Russ. Math. Surv. 76, No. 5, 745-819 (2021); translation from Usp. Mat. Nauk 76, No. 5, 3-80 (2021). MSC: 81Q20 35L15 35L45 35S10 53D12 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. Math. Surv. 76, No. 5, 745--819 (2021; Zbl 1492.81056); translation from Usp. Mat. Nauk 76, No. 5, 3--80 (2021) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. Representation of Bessel functions by the Maslov canonical operator. (English. Russian original) Zbl 1471.81033 Theor. Math. Phys. 208, No. 2, 1018-1037 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 196-217 (2021). MSC: 81Q20 81S08 33C10 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 208, No. 2, 1018--1037 (2021; Zbl 1471.81033); translation from Teor. Mat. Fiz. 208, No. 2, 196--217 (2021) Full Text: DOI
Dobrokhotov, Sergei; Nazaikinskii, Vladimir Fock quantization of canonical transformations and semiclassical asymptotics for degenerate problems. (English) Zbl 1472.81099 Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 – July 6, 2019. Cham: Birkhäuser. Trends Math., 187-195 (2020). MSC: 81Q20 35L80 81S10 53D12 53D22 PDFBibTeX XMLCite \textit{S. Dobrokhotov} and \textit{V. Nazaikinskii}, in: Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 -- July 6, 2019. Cham: Birkhäuser. 187--195 (2020; Zbl 1472.81099) Full Text: DOI
Chernyshev, V. L.; Hilberdink, T. W.; Nazaikinskii, V. E. Asymptotics of the number of restricted partitions. (English) Zbl 1469.11387 Russ. J. Math. Phys. 27, No. 4, 456-468 (2020). MSC: 11N45 11P81 05A17 PDFBibTeX XMLCite \textit{V. L. Chernyshev} et al., Russ. J. Math. Phys. 27, No. 4, 456--468 (2020; Zbl 1469.11387) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. (English. Russian original) Zbl 1483.53094 Math. Notes 108, No. 3, 318-338 (2020); translation from Mat. Zametki 108, No. 3, 334-359 (2020). MSC: 53D12 41A60 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 108, No. 3, 318--338 (2020; Zbl 1483.53094); translation from Mat. Zametki 108, No. 3, 334--359 (2020) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. (English. Russian original) Zbl 1450.35119 Comput. Math. Math. Phys. 60, No. 8, 1348-1360 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394-1407 (2020). MSC: 35G10 35Q35 35Q41 35Q61 81Q20 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Comput. Math. Math. Phys. 60, No. 8, 1348--1360 (2020; Zbl 1450.35119); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394--1407 (2020) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. (English. Russian original) Zbl 1441.81091 Theor. Math. Phys. 201, No. 3, 1742-1770 (2019); translation from Teor. Mat. Fiz. 201, No. 3, 382-414 (2019). MSC: 81Q10 81Q20 33C10 34L40 34E10 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Theor. Math. Phys. 201, No. 3, 1742--1770 (2019; Zbl 1441.81091); translation from Teor. Mat. Fiz. 201, No. 3, 382--414 (2019) Full Text: DOI
Chernyshev, V. L.; Minenkov, D. S.; Nazaikinskii, V. E. Typical shape of elements in an arithmetical semigroup with exponentially growing prime counting function and deviations from the Bose-Einstein distribution. (English) Zbl 1439.11260 Math. Notes 104, No. 6, 939-942 (2018). MSC: 11N45 11N80 PDFBibTeX XMLCite \textit{V. L. Chernyshev} et al., Math. Notes 104, No. 6, 939--942 (2018; Zbl 1439.11260) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. (English. Russian original) Zbl 1420.35151 Math. Notes 104, No. 4, 471-488 (2018); translation from Mat. Zametki 104, No. 4, 483-504 (2018). MSC: 35L20 35B40 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Math. Notes 104, No. 4, 471--488 (2018; Zbl 1420.35151); translation from Mat. Zametki 104, No. 4, 483--504 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, Anna V. One approach to the computation of asymptotics of integrals of rapidly varying functions. (English. Russian original) Zbl 1397.42004 Math. Notes 103, No. 5, 713-723 (2018); translation from Mat. Zametki 103, No. 5, 680-692 (2018). MSC: 42B20 41A60 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Notes 103, No. 5, 713--723 (2018; Zbl 1397.42004); translation from Mat. Zametki 103, No. 5, 680--692 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. On the asymptotics of a Bessel-type integral having applications in wave run-up theory. (English. Russian original) Zbl 1384.42001 Math. Notes 102, No. 6, 756-762 (2017); translation from Mat. Zametki 102, No. 6, 828-835 (2017). MSC: 42A38 35L05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 102, No. 6, 756--762 (2017; Zbl 1384.42001); translation from Mat. Zametki 102, No. 6, 828--835 (2017) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Rouleux, M. The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. (English. Russian original) Zbl 1377.35062 Dokl. Math. 96, No. 1, 406-410 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 6, 624-628 (2016). MSC: 35J05 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Dokl. Math. 96, No. 1, 406--410 (2017; Zbl 1377.35062); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 6, 624--628 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. (English. Russian original) Zbl 1516.35040 Math. Notes 101, No. 6, 1053-1060 (2017); translation from Mat. Zametki 101, No. 6, 936-942 (2017). MSC: 35B25 35C20 35Q35 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 101, No. 6, 1053--1060 (2017; Zbl 1516.35040); translation from Mat. Zametki 101, No. 6, 936--942 (2017) Full Text: DOI
Minenkov, D. S.; Nazaikinskiĭ, V. E.; Chernyshev, V. L. On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators. (English. Russian original) Zbl 1366.11105 Funct. Anal. Appl. 50, No. 4, 291-307 (2016); translation from Funkts. Anal. Prilozh. 50, No. 4, 55-75 (2016). MSC: 11N45 11N80 PDFBibTeX XMLCite \textit{D. S. Minenkov} et al., Funct. Anal. Appl. 50, No. 4, 291--307 (2016; Zbl 1366.11105); translation from Funkts. Anal. Prilozh. 50, No. 4, 55--75 (2016) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. (English. Russian original) Zbl 1362.35170 Math. Notes 100, No. 5, 695-713 (2016); translation from Mat. Zametki 100, No. 5, 710-731 (2016). MSC: 35L20 35L80 35B40 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 100, No. 5, 695--713 (2016; Zbl 1362.35170); translation from Mat. Zametki 100, No. 5, 710--731 (2016) Full Text: DOI
Minenkov, D. S.; Nazaikinskiĭ, V. E. Remark on the inverse abstract prime number theorem. (English. Russian original) Zbl 1354.11062 Math. Notes 100, No. 4, 633-635 (2016); translation from Mat. Zametki 100, No. 4, 627-629 (2016). MSC: 11N37 11N80 PDFBibTeX XMLCite \textit{D. S. Minenkov} and \textit{V. E. Nazaikinskiĭ}, Math. Notes 100, No. 4, 633--635 (2016; Zbl 1354.11062); translation from Mat. Zametki 100, No. 4, 627--629 (2016) Full Text: DOI
Nazaikinskii, V. E. The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary. (English. Russian original) Zbl 1330.53108 Math. Notes 96, No. 2, 248-260 (2014); translation from Mat. Zametki 96, No. 2, 261-276 (2014). Reviewer: Chengbo Wang (Hangzhou) MSC: 53D12 35L05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 96, No. 2, 248--260 (2014; Zbl 1330.53108); translation from Mat. Zametki 96, No. 2, 261--276 (2014) Full Text: DOI
Nazaikinskii, V. E. On the representation of localized functions in \(\mathbb R^2\) by the Maslov canonical operator. (English. Russian original) Zbl 1320.53100 Math. Notes 96, No. 1, 99-109 (2014); translation from Mat. Zametki 96, No. 1, 88-100 (2014). MSC: 53D12 35L05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 96, No. 1, 99--109 (2014; Zbl 1320.53100); translation from Mat. Zametki 96, No. 1, 88--100 (2014) Full Text: DOI
Dobrokhotov, S. Yu.; Makrakis, G. N.; Nazaikinskii, V. E.; Tudorovskii, T. Ya. New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. (English. Russian original) Zbl 1298.81091 Theor. Math. Phys. 177, No. 3, 1579-1605 (2013); translation from Teor. Mat. Fiz. 177, No. 3, 355-386 (2013). MSC: 81Q20 81Q05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Theor. Math. Phys. 177, No. 3, 1579--1605 (2013; Zbl 1298.81091); translation from Teor. Mat. Fiz. 177, No. 3, 355--386 (2013) Full Text: DOI arXiv
Dobrokhotov, S. Yu.; Lozhnikov, D. A.; Nazaikinskii, V. E. Wave trains associated with a cascade of bifurcations of space-time caustics over elongated underwater banks. (English) Zbl 1338.35390 Math. Model. Nat. Phenom. 8, No. 5, 1-12 (2013). MSC: 35Q53 76B15 35A18 35B40 37G10 74J05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Model. Nat. Phenom. 8, No. 5, 1--12 (2013; Zbl 1338.35390) Full Text: DOI
Nazaikinskii, V. E. On the asymptotics of the number of states for the Bose-Maslov gas. (English) Zbl 1285.82048 Math. Notes 91, No. 6, 816-823 (2012). MSC: 82D05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 91, No. 6, 816--823 (2012; Zbl 1285.82048) Full Text: DOI
Nazaikinskii, V. E. Degenerate wave equation with localized initial data: asymptotic solutions corresponding to various self-adjoint extensions. (English. Russian original) Zbl 1234.35149 Math. Notes 89, No. 5, 749-753 (2011); translation from Mat. Zametki 89, No. 5, 797-800 (2011). MSC: 35L80 35L15 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii}, Math. Notes 89, No. 5, 749--753 (2011; Zbl 1234.35149); translation from Mat. Zametki 89, No. 5, 797--800 (2011) Full Text: DOI
Dubnov, Vladimir L.; Maslov, Victor P.; Nazaikinskii, Vladimir E. The complex Lagrangian germ and the canonical operator. (English) Zbl 0920.58051 Russ. J. Math. Phys. 3, No. 2, 141-190 (1995); errata ibid. 4, No. 2, 271 (1996). Reviewer: W.M.Oliva (Lisboa) MSC: 58J37 35Q58 58J40 PDFBibTeX XMLCite \textit{V. L. Dubnov} et al., Russ. J. Math. Phys. 3, No. 2, 1 (1995; Zbl 0920.58051) Full Text: arXiv
Nazaĭkinskiĭ, V. E.; Sternin, B. Yu.; Shatalov, V. E. On an application of the Maslov operator method to a diffraction problem. (English. Russian original) Zbl 0788.35024 Sov. Math., Dokl. 43, No. 2, 547-549 (1991); translation from Dokl. Akad. Nauk SSSR 317, No. 4, 832-834 (1991). MSC: 35G10 78A45 78A05 PDFBibTeX XMLCite \textit{V. E. Nazaĭkinskiĭ} et al., Sov. Math., Dokl. 43, No. 2, 547--549 (1991; Zbl 0788.35024); translation from Dokl. Akad. Nauk SSSR 317, No. 4, 832--834 (1991)
Maslov, V. P.; Nazaĭkinskiĭ, V. E. Algebras with general commutation relations and their applications. I: Pseudodifferential equations with increasing coefficients. (English. Russian original) Zbl 0482.58028 J. Sov. Math. 15, 167-273 (1981); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 13, 5-144 (1979). MSC: 58J40 35B40 47A60 35S05 81Q10 81S05 PDFBibTeX XMLCite \textit{V. P. Maslov} and \textit{V. E. Nazaĭkinskiĭ}, J. Sov. Math. 15, 167--273 (1979; Zbl 0482.58028); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 13, 5--144 (1979) Full Text: DOI