Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory
The paper is devoted to describing the dynamics and uprush of time-periodic long waves in basins with gentle shores. We consider waves that are defined by solutions localized between caustics in the domain bounded by the shores of the basin. We also consider solutions localized in the vicinity of a...
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| Published in | Russian journal of mathematical physics Vol. 30; no. 4; pp. 543 - 551 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Moscow
Pleiades Publishing
01.12.2023
Springer Nature B.V |
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| Abstract | The paper is devoted to describing the dynamics and uprush of time-periodic long waves in basins with gentle shores. We consider waves that are defined by solutions localized between caustics in the domain bounded by the shores of the basin. We also consider solutions localized in the vicinity of a periodic trajectory which, during the period, has exactly two intersections with the boundary of such a domain.
DOI
10.1134/S1061920823040106 |
|---|---|
| AbstractList | The paper is devoted to describing the dynamics and uprush of time-periodic long waves in basins with gentle shores. We consider waves that are defined by solutions localized between caustics in the domain bounded by the shores of the basin. We also consider solutions localized in the vicinity of a periodic trajectory which, during the period, has exactly two intersections with the boundary of such a domain.
DOI
10.1134/S1061920823040106 The paper is devoted to describing the dynamics and uprush of time-periodic long waves in basins with gentle shores. We consider waves that are defined by solutions localized between caustics in the domain bounded by the shores of the basin. We also consider solutions localized in the vicinity of a periodic trajectory which, during the period, has exactly two intersections with the boundary of such a domain. DOI 10.1134/S1061920823040106 |
| Author | Tsvetkova, A.V. Klevin, A.I. |
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| References | AnikinA. Yu.DobrokhotovS. Yu.NazaikinskiiV. E.TsvetkovaA. V.Asymptotic Eigenfunctions of the Operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla D(x) \nabla$$\end{document} Defined in a Two-Dimensional Domain and Degenerating on Its Boundary and Billiards with Semi-Rigid WallsDiffer. Eq.2019555644657397653310.1134/S0012266119050069 AnikinA. Yu.DobrokhotovS. Yu.NazaikinskiiV. E.Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up ProblemMath. Notes20181044471488385938510.1134/S0001434618090158 NazaikinskiiV. E.The Maslov Canonical Operator on Lagrangian Manifolds in the Phase Space Corresponding to a Wave Equation Degenerating on the BoundaryMath. Notes2014962248260334429410.1134/S0001434614070268 KlevinA. I.Asymptotic Behavior of Bouncing Ball Type Eigenfunctions of the Operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla D(x) \nabla$$\end{document} in a Domain Bounded by Semi-Rigid WallsDiffer. Eq.20215722352544237011 StokerJ. J.Water Waves: The Mathematical Theory with Applications1958New YorkJohn Wiley and Sons PelinovskyE. N.MazovaR. Kh.Exact Analytical Solutions of Nonlinear Problems of Tsunami Wave Run-Up on Slopes with Different ProfiesNatural Hazards19926322724910.1007/BF00129510 AnikinA. Yu.DobrokhotovS. Yu.NazaikinskiiV. E.TsvetkovaA. V.Nonstandard Liouville Tori and Caustics in Asymptotics in the Form of Airy and Bessel Functions for Two-Dimensional Standing Coastal WavesSt. Petersburg Mathematical Journal2022332185205444575510.1090/spmj/1696 MatveevV. S.The Asymptotic Eigenfunctions of the Operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla D(x, y)\nabla$$\end{document} Corresponding to Liouville Metrics and Waves on Water Captured by Bottom IrregularitiesMath. Notes1998643357363168020510.1007/BF02314845 MusakL. A.BlondP. H. LeWaves in the Ocean1978Amsterdam etc. TaimanovI. A.On First Integrals of Geodesic Flows on a Two-Dimensional TorusProc. Steklov Inst. Math.20162951225-тАУ242362852510.1134/S0081543816080150 DobrokhotovS. Yu.MinenkovD. S.NazaikinskiiV. E.Asymptotic Solutions of the Cauchy Problem for the Nonlinear Shallow Water Equations in a Basin with a Gently Sloping BeachRuss. J. Math. Phys.20222912836439850410.1134/S1061920822010034 MaslovV. P.FedoriukM. V. Semiclassical Approximation in Quantum Mechanics1981Dordrecht-Boston, Mass.D. Reidel Publishing Co.10.1007/978-94-009-8410-3 MeiC. C.The Applied Dynamics of Ocean Surface Waves. World Scientific1989Singapore SretenskiiL. N.Theory of Fluid Wave Motions1977MoscowNauka MaslovV. P.The Complex WKB Method for Nonlinear Equations I1994BaselBirkhäuser10.1007/978-3-0348-8536-2 OleinikO. A.RadkevichV. E.Second Order Equations with Nonnegative Characteristic Form1973New YorkAmerican Mathematical Society, Providence, Rhode Island and Plenum Press10.1007/978-1-4684-8965-1 S. Yu. Dobrokhotov (5170_CR5) 2022; 29 C. C. Mei (5170_CR4) 1989 I. A. Taimanov (5170_CR13) 2016; 295 L. N. Sretenskii (5170_CR2) 1977 V. P. Maslov (5170_CR8) 1994 O. A. Oleinik (5170_CR9) 1973 A. I. Klevin (5170_CR16) 2021; 57 V. P. Maslov (5170_CR7) 1981 A. Yu. Anikin (5170_CR14) 2019; 55 A. Yu. Anikin (5170_CR15) 2022; 33 E. N. Pelinovsky (5170_CR6) 1992; 6 A. Yu. Anikin (5170_CR11) 2018; 104 J. J. Stoker (5170_CR1) 1958 V. E. Nazaikinskii (5170_CR10) 2014; 96 V. S. Matveev (5170_CR12) 1998; 64 L. A. Musak (5170_CR3) 1978 |
| References_xml | – volume: 29 start-page: 28 issue: 1 year: 2022 ident: 5170_CR5 publication-title: Russ. J. Math. Phys. doi: 10.1134/S1061920822010034 contributor: fullname: S. Yu. Dobrokhotov – volume: 96 start-page: 248 issue: 2 year: 2014 ident: 5170_CR10 publication-title: Math. Notes doi: 10.1134/S0001434614070268 contributor: fullname: V. E. Nazaikinskii – volume-title: Waves in the Ocean year: 1978 ident: 5170_CR3 contributor: fullname: L. A. Musak – volume: 55 start-page: 644 issue: 5 year: 2019 ident: 5170_CR14 publication-title: Differ. Eq. doi: 10.1134/S0012266119050069 contributor: fullname: A. Yu. Anikin – volume-title: Theory of Fluid Wave Motions year: 1977 ident: 5170_CR2 contributor: fullname: L. N. Sretenskii – volume-title: Semiclassical Approximation in Quantum Mechanics year: 1981 ident: 5170_CR7 doi: 10.1007/978-94-009-8410-3 contributor: fullname: V. P. Maslov – volume: 295 start-page: 225-тАУ242 issue: 1 year: 2016 ident: 5170_CR13 publication-title: Proc. Steklov Inst. Math. doi: 10.1134/S0081543816080150 contributor: fullname: I. A. Taimanov – volume: 33 start-page: 185 issue: 2 year: 2022 ident: 5170_CR15 publication-title: St. Petersburg Mathematical Journal doi: 10.1090/spmj/1696 contributor: fullname: A. Yu. Anikin – volume: 64 start-page: 357 issue: 3 year: 1998 ident: 5170_CR12 publication-title: Math. Notes doi: 10.1007/BF02314845 contributor: fullname: V. S. Matveev – volume-title: The Applied Dynamics of Ocean Surface Waves. World Scientific year: 1989 ident: 5170_CR4 contributor: fullname: C. C. Mei – volume: 104 start-page: 471 issue: 4 year: 2018 ident: 5170_CR11 publication-title: Math. Notes doi: 10.1134/S0001434618090158 contributor: fullname: A. Yu. Anikin – volume: 6 start-page: 227 issue: 3 year: 1992 ident: 5170_CR6 publication-title: Natural Hazards doi: 10.1007/BF00129510 contributor: fullname: E. N. Pelinovsky – volume: 57 start-page: 235 issue: 2 year: 2021 ident: 5170_CR16 publication-title: Differ. Eq. contributor: fullname: A. I. Klevin – volume-title: The Complex WKB Method for Nonlinear Equations I year: 1994 ident: 5170_CR8 doi: 10.1007/978-3-0348-8536-2 contributor: fullname: V. P. Maslov – volume-title: Second Order Equations with Nonnegative Characteristic Form year: 1973 ident: 5170_CR9 doi: 10.1007/978-1-4684-8965-1 contributor: fullname: O. A. Oleinik – volume-title: Water Waves: The Mathematical Theory with Applications year: 1958 ident: 5170_CR1 contributor: fullname: J. J. Stoker |
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| Title | Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory |
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