Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. Nonlinear effects and run-up of coastal waves generated by billiards with semi-rigid walls in the framework of shallow water theory. (English. Russian original) Zbl 07781666 Proc. Steklov Inst. Math. 322, 105-117 (2023); translation from Tr. Mat. Inst. Steklova 322, 111-123 (2023). MSC: 76B15 76M45 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Proc. Steklov Inst. Math. 322, 105--117 (2023; Zbl 07781666); translation from Tr. Mat. Inst. Steklova 322, 111--123 (2023) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniformization and semiclassical asymptotics for a class of equations degenerating on the boundary of a manifold. (English. Russian original) Zbl 1512.35066 J. Math. Sci., New York 270, No. 4, 507-530 (2023); translation from Probl. Mat. Anal. 122, 5-24 (2023). MSC: 35B40 53D12 76B15 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., J. Math. Sci., New York 270, No. 4, 507--530 (2023; Zbl 1512.35066); translation from Probl. Mat. Anal. 122, 5--24 (2023) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E. Asymptotic solutions of the Cauchy problem for the nonlinear shallow water equations in a basin with a gently sloping beach. (English) Zbl 1490.76035 Russ. J. Math. Phys. 29, No. 1, 28-36 (2022). MSC: 76B15 35Q35 35B40 76M45 35B27 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 29, No. 1, 28--36 (2022; Zbl 1490.76035) Full Text: DOI
Nazaikinskii, Vladimir E.; Bedrikovetsky, Pavel G.; Kuzmina, Liudmila I.; Osipov, Yuri V. Exact solution for deep bed filtration with finite blocking time. (English) Zbl 1486.76079 SIAM J. Appl. Math. 80, No. 5, 2120-2143 (2020). MSC: 76S05 76T20 35Q35 65M25 PDFBibTeX XMLCite \textit{V. E. Nazaikinskii} et al., SIAM J. Appl. Math. 80, No. 5, 2120--2143 (2020; Zbl 1486.76079) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. (English. Russian original) Zbl 1455.76019 Math. Notes 107, No. 5, 847-853 (2020); translation from Mat. Zametki 107, No. 5, 780-786 (2020). MSC: 76B15 76M45 35Q35 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Math. Notes 107, No. 5, 847--853 (2020; Zbl 1455.76019); translation from Mat. Zametki 107, No. 5, 780--786 (2020) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source. (English) Zbl 1448.35391 Russ. J. Math. Phys. 27, No. 2, 185-191 (2020). MSC: 35Q35 35S10 76B15 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 27, No. 2, 185--191 (2020; Zbl 1448.35391) Full Text: DOI
Karaeva, D. A.; Karaev, A. D.; Nazaikinskii, V. E. Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom. (English. Russian original) Zbl 1418.76043 Differ. Equ. 54, No. 8, 1057-1072 (2018); translation from Differ. Uravn. 54, No. 8, 1075-1089 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 76M50 76B15 76M45 PDFBibTeX XMLCite \textit{D. A. Karaeva} et al., Differ. Equ. 54, No. 8, 1057--1072 (2018; Zbl 1418.76043); translation from Differ. Uravn. 54, No. 8, 1075--1089 (2018) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E. Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides. (English) Zbl 1388.76028 Russ. J. Math. Phys. 25, No. 1, 1-16 (2018). MSC: 76B07 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} and \textit{V. E. Nazaikinskii}, Russ. J. Math. Phys. 25, No. 1, 1--16 (2018; Zbl 1388.76028) Full Text: DOI
Lozhnikov, D. A.; Nazaĭkinskiĭ, V. E. Method for the analysis of long water waves taking into account reflection from a gently sloping beach. (English. Russian original) Zbl 1440.76014 J. Appl. Math. Mech. 81, No. 1, 21-28 (2017); translation from Prikl. Mat. Mekh. 81, No. 1, 33-44 (2017). MSC: 76B15 76-04 PDFBibTeX XMLCite \textit{D. A. Lozhnikov} and \textit{V. E. Nazaĭkinskiĭ}, J. Appl. Math. Mech. 81, No. 1, 21--28 (2017; Zbl 1440.76014); translation from Prikl. Mat. Mekh. 81, No. 1, 33--44 (2017) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge. (English) Zbl 1432.76203 Russ. J. Math. Phys. 24, No. 4, 544-552 (2017). MSC: 76M35 76B15 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 24, No. 4, 544--552 (2017; Zbl 1432.76203) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A. Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. (English. Russian original) Zbl 1372.35180 Math. Notes 101, No. 5, 802-814 (2017); translation from Mat. Zametki 101, No. 5, 700-715 (2017). MSC: 35L20 76E20 86A05 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Math. Notes 101, No. 5, 802--814 (2017; Zbl 1372.35180); translation from Mat. Zametki 101, No. 5, 700--715 (2017) Full Text: DOI
Dobrokhotov, S. Yu.; Minenkov, D. S.; Nazaikinskii, V. E.; Tirozzi, B. Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. (English) Zbl 1329.35246 Agliari, Elena (ed.) et al., Theory and applications in mathematical physics. Conference in honor of B. Tirozzi’s 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4713-27-6/hbk; 978-981-4713-29-0/ebook). 29-47 (2016). MSC: 35Q35 76B15 76M45 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., in: Theory and applications in mathematical physics. Conference in honor of B. Tirozzi's 70th birthday. Hackensack, NJ: World Scientific. 29--47 (2016; Zbl 1329.35246) Full Text: DOI
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. Two-dimensional wave equation with degeneration on the curvilinear boundary of the domain and asymptotic solutions with localized initial data. (English) Zbl 1320.35180 Russ. J. Math. Phys. 20, No. 4, 389-401 (2013). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L15 35L05 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 20, No. 4, 389--401 (2013; Zbl 1320.35180) Full Text: DOI
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
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tirozzi, B. Asymptotic solution of the one-dimensional wave equation with localized initial data and with degenerating velocity. I. (English) Zbl 1387.35404 Russ. J. Math. Phys. 17, No. 4, 434-447 (2010). MSC: 35L60 35C20 35Q35 76B15 PDFBibTeX XMLCite \textit{S. Yu. Dobrokhotov} et al., Russ. J. Math. Phys. 17, No. 4, 434--447 (2010; Zbl 1387.35404) Full Text: DOI
Nazaikinskij, V. E.; Sternin, B. Yu.; Shatalov, V. E. Introduction to Maslov’s operational method (applications). (English) Zbl 0827.35006 Borisovich, Yu. G. (ed.), Problems of geometry, topology and mathematical physics. Voronezh: Izdatel’stvo Voronezhskogo Universiteta. Nov. Global’nom Anal. 51-64 (1992). MSC: 35A25 76X05 PDFBibTeX XMLCite \textit{V. E. Nazaikinskij} et al., in: Zadachi geometrii, topologii i matematicheskoj fiziki. Voronezh: Izdatel'stvo Voronezhskogo Universiteta. 51--64 (1992; Zbl 0827.35006)