V. S. Matveev, “The asymptotic eigenfunctions of the operator $\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities”, Mat. Zametki, 64:3 (1998), 414–422; Math. Notes, 64:3 (1998), 357

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Matematicheskie Zametki, 1998, Volume 64, Issue 3, Pages 414–422
DOI: https://doi.org/10.4213/mzm1412 (Mi mzm1412)

This article is cited in 12 scientific papers (total in 12 papers)

The asymptotic eigenfunctions of the operator

$\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities

V. S. Matveev

Chelyabinsk State University

Full-text PDF (1201 kB) Citations (12)

References:

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DOI: https://doi.org/10.4213/mzm1412

Abstract: We construct a set of examples of bottom reliefs for which there exist captured waves corresponding to quasimodes of the wave operator

$\nabla D(x,y)\nabla$ .

Received: 01.04.1997

English version:
Mathematical Notes, 1998, Volume 64, Issue 3, Pages 357–363
DOI: https://doi.org/10.1007/BF02314845

Bibliographic databases:

UDC: 551.46+514.17+517.9

Language: Russian

Citation: V. S. Matveev, “The asymptotic eigenfunctions of the operator

$\nabla D(x,y)\nabla$ corresponding to Liouville metrics and waves on water captured by bottom irregularities”, Mat. Zametki, 64:3 (1998), 414–422; Math. Notes, 64:3 (1998), 357–363

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1412

https://doi.org/10.4213/mzm1412

https://www.mathnet.ru/eng/mzm/v64/i3/p414

This publication is cited in the following 12 articles:

Vladislav Rykhlov, Anatoly Anikin, “High-frequency two-dimensional asymptotic standing coastal trapped waves in nearly integrable case”, Lett Math Phys, 115:1 (2025)
A.I. Klevin, A.V. Tsvetkova, “Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory”, Russ. J. Math. Phys., 30:4 (2023), 543
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for two-dimensional standing coastal waves”, St. Petersburg Math. J., 33:2 (2022), 185–205
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Asymptotics, Related to Billiards with Semi-Rigid Walls, of Eigenfunctions of the $\nabla D(x)\nabla$ Operator in Dimension 2 and Trapped Coastal Waves”, Math. Notes, 105:5 (2019), 789–794
Anikin A.Yu. Dobrokhotov S.Yu. Nazaikinskii V.E. Tsvetkova A.V., “Asymptotic Eigenfunctions of the Operator Delta D(X)Delta Defined in a Two-Dimensional Domain and Degenerating on Its Boundary and Billiards With Semi-Rigid Walls”, Differ. Equ., 55:5 (2019), 644–657
Dobrokhotov S.Yu. Nazaikinskii V.E., “Asymptotic Localized Solutions of the Shallow Water Equations Over a Nonuniform Bottom”, AIP Conference Proceedings, 2048, ed. Pasheva V. Popivanov N. Venkov G., Amer Inst Physics, 2018, 040026
Mikes J. Stepanova E. Vanzurova A., “Differential Geometry of Special Mappings”, Differential Geometry of Special Mappings, Palacky Univ, 2015, 1–566
Dobrokhotov S.Yu. Lozhnikov D.A. Vargas C.A., “Asymptotics of Waves on the Shallow Water Generated by Spatially-Localized Sources and Trapped by Underwater Ridges”, Russ. J. Math. Phys., 20:1 (2013), 11–24
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”, Math. Model. Nat. Phenom., 8:5 (2013), 1–12
Matveev V.S., “Pseudo-Riemannian Metrics on Closed Surfaces Whose Geodesic Flows Admit Nontrivial Integrals Quadratic in Momenta, and Proof of the Projective Obata Conjecture for Two-Dimensional Pseudo-Riemannian Metrics”, J. Math. Soc. Jpn., 64:1 (2012), 107–152
Dobrokhotov S. Rouleux M., “The Semi-Classical Maupertuis-Jacobi Correspondence for Quasi-Periodic Hamiltonian Flows with Applications to Linear Water Waves Theory”, Asymptotic Anal., 74:1-2 (2011), 33–73
S. Yu. Dobrokhotov, M. Rouleux, “The Semiclassical Maupertuis–Jacobi Correspondence and Applications to Linear Water Waves Theory”, Math. Notes, 87:3 (2010), 430–435

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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