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Mat. Zametki, 2017, Volume 101, Issue 6, Pages 936–943 (Mi mz11493)  

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

Brief Communications

Punctured Lagrangian manifolds and asymptotic solutions of linear water wave equations with localized initial conditions

S. Yu. Dobrokhotovab, V. E. Nazaikinskiiab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Keywords: Cauchy–Poisson problem, water waves, localized initial conditions, asymptotics, Maslov's canonical operator

Funding Agency Grant Number
Russian Science Foundation 16-11-10282
This work was supported by the Russian Science Foundation under grant 16-11-10282.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11493

Full text: PDF file (422 kB)
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English version:
Mathematical Notes, 2017, 101:6, 1053–1060

Bibliographic databases:

Received: 01.12.2016

Citation: S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Punctured Lagrangian manifolds and asymptotic solutions of linear water wave equations with localized initial conditions”, Mat. Zametki, 101:6 (2017), 936–943; Math. Notes, 101:6 (2017), 1053–1060

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Sergeev, “Asymptotic Solutions of the One-Dimensional Linearized Korteweg–de Vries Equation with Localized Initial Data”, Math. Notes, 102:3 (2017), 403–416  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. I. Allilueva, A. I. Shafarevich, “Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics”, Math. Notes, 102:6 (2017), 737–745  mathnet  crossref  crossref  isi  elib
    3. S. Ya. Sekerzh-Zen'kovich, “Estimation of accuracy of an asymptotic solution of the generalized Cauchy problem for the Boussinesq equation as applied to the potential model of tsunami with a ‘simple’ source”, Russ. J. Math. Phys., 24:4 (2017), 526–533  crossref  mathscinet  zmath  isi  scopus
    4. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Asymptotics of linear water waves generated by a localized source near the focal points on the leading edge”, Russ. J. Math. Phys., 24:4 (2017), 544–552  crossref  mathscinet  zmath  isi  scopus
    5. S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen'kovich, A. A. Tolchennikov, “Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom”, Russ. J. Math. Phys., 24:3 (2017), 310–321  crossref  mathscinet  zmath  isi  scopus
    6. A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “Asymptotics of Green function for the linear waves equations in a domain with a non-uniform bottom”, Proceedings of the International Conference Days on Diffraction (DD) 2017, IEEE, 2017, 18–23  isi
    7. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Waves on the free surface described by linearized equations of hydrodynamics with localized right-hand sides”, Russ. J. Math. Phys., 25:1 (2018), 1–16  crossref  mathscinet  zmath  isi  scopus
    8. S. A. Sergeev, “Asymptotic Solutions of One-Dimensional Linear Evolution Equations for Surface Waves with Account for Surface Tension”, Math. Notes, 103:3 (2018), 499–504  mathnet  crossref  crossref  isi  elib
    9. A. Anikin, S. Dobrokhotov, V. Nazaikinskii, M. Rouleux, “Semi-classical Green functions”, 2018 Days on Diffraction (DD), IEEE, 2018, 17–23  isi
    10. A. A. Tolchennikov, “Behavior of the solution of the Klein–Gordon equation with a localized initial condition”, Theoret. and Math. Phys., 199:2 (2019), 761–770  mathnet  crossref  elib
    11. Sekerzh-Zen'kovich S.Ya., Tolchennikov A.A., “Application of An Asymptotic Solution of the Problem of Linear Wave Propagation on Water to the Approximation of Tsunami Mareograms of 2011 Obtained At Two Dart Stations”, Russ. J. Math. Phys., 26:1 (2019), 70–74  crossref  mathscinet  isi  scopus
    12. Dobrokhotov S.Yu. Tolchennikov A.A., “Solution of the Two-Dimensional Dirac Equation With a Linear Potential and a Localized Initial Condition”, Russ. J. Math. Phys., 26:2 (2019), 139–151  crossref  isi
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