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
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.; Tsvetkova, A. V. Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves. (English. Russian original) Zbl 1485.35307 St. Petersbg. Math. J. 33, No. 2, 185-205 (2022); translation from Algebra Anal. 33, No. 2, 5-34 (2021). MSC: 35P20 35B40 35J25 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., St. Petersbg. Math. J. 33, No. 2, 185--205 (2022; Zbl 1485.35307); translation from Algebra Anal. 33, No. 2, 5--34 (2021) 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
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the \(\nabla D(x)\nabla\) operator in dimension 2 and trapped coastal waves. (English. Russian original) Zbl 1426.37049 Math. Notes 105, No. 5, 789-794 (2019); translation from Mat. Zametki 105, No. 5, 792-797 (2019). MSC: 37J35 37J10 34L10 34L20 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Math. Notes 105, No. 5, 789--794 (2019; Zbl 1426.37049); translation from Mat. Zametki 105, No. 5, 792--797 (2019) Full Text: DOI
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tsvetkova, A. V. Asymptotic eigenfunctions of the operator \(\nabla D(x)\nabla\) defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls. (English. Russian original) Zbl 1418.37094 Differ. Equ. 55, No. 5, 644-657 (2019); translation from Differ. Uravn. 55, No. 5, 660-672 (2019). MSC: 37J35 37J05 37D50 53D12 53D25 35P05 PDFBibTeX XMLCite \textit{A. Yu. Anikin} et al., Differ. Equ. 55, No. 5, 644--657 (2019; Zbl 1418.37094); translation from Differ. Uravn. 55, No. 5, 660--672 (2019) 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