S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen'kovich, “A Class of Exact Algebraic Localized Solutions of the Multidimensional Wave Equation”, Mat. Zametki, 88:6 (2010), 942–945; Math. Notes, 88:6 (2010), 894

Citation in format AMSBIB

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\paper A Class of Exact Algebraic Localized Solutions of the Multidimensional Wave Equation

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\pages 942--945

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\jour Math. Notes

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D Tseluiko, N S Alharthi, R Barros, K R Khusnutdinova, “Internal ring waves in a three-layer fluid on a current with a constant vertical shear”, Nonlinearity, 36:6 (2023), 3431
Maxim Shishlenin, Nikita Savchenko, Nikita Novikov, Dmitriy Klyuchinskiy, “Modeling of 2D Acoustic Radiation Patterns as a Control Problem”, Mathematics, 10:7 (2022), 1116
S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Math. Surveys, 76:5 (2021), 745–819
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V. M. Babich, “Prilozhenie funktsii Adamara k matematicheskomu opisaniyu volny tsunami, voznikshei ot lokalizovannogo istochnika”, Matematicheskie voprosy teorii rasprostraneniya voln. 50, Posvyaschaetsya devyanostoletiyu Vasiliya Mikhailovicha BABIChA, Zap. nauchn. sem. POMI, 493, POMI, SPb., 2020, 22–28
A. S. Blagoveshchenskii, A. P. Kiselev, “Bateman–Hörmander Two-Dimensional Waves with a Singularity at a Running Point”, Math. Notes, 106:5 (2019), 846–849
A. A. Tolchennikov, “Simple exact solutions and asymptotic localized solutions of the two-dimensional massless Dirac equation for graphene”, Theoret. and Math. Phys., 196:1 (2018), 996–1001
A. V. Aksenov, S. Yu. Dobrokhotov, K. P. Druzhkov, “Exact Step-Like Solutions of One-Dimensional Shallow-Water Equations over a Sloping Bottom”, Math. Notes, 104:6 (2018), 915–921
Dobrokhotov S.Yu., Nazaikinskii V.E., “Asymptotic Localized Solutions of the Shallow Water Equations Over a Nonuniform Bottom”, AIP Conference Proceedings, 2048, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2018, 040026
P. S. Petrov, S. A. Sergeev, A. A. Tolchennikov, “Modeling of Pulse Signals in 3D Propagation Problems of Deep-Water Acoustics Based on the Modified Maslov's Canonical Operator”, Russ. J. Math. Phys., 25:1 (2018), 102
S. A. Sergeev, A. A. Tolchennikov, “Creation Operators in the Problem of Localized Solutions of the Linearized Shallow Water Equations with Regular and Singular Characteristics”, Math. Notes, 100:6 (2016), 852–861
Khusnutdinova K.R., Zhang X., “Nonlinear ring waves in a two-layer fluid”, Physica D, 333:SI (2016), 208–221
Yu. A. Chirkunov, S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms”, Theoret. and Math. Phys., 178:3 (2014), 278–298
V. E. Nazaikinskii, “On the Representation of Localized Functions in $\mathbb R^2$ by Maslov's Canonical Operator”, Math. Notes, 96:1 (2014), 99–109
S. Yu. Dobrokhotov, S. B. Medvedev, D. S. Minenkov, “On Replacements Reducing One-Dimensional Systems of Shallow-Water Equations to the Wave Equation with Sound Speed $c^2=x$ ”, Math. Notes, 93:5 (2013), 704–714
V. V. Grushin, S. Yu. Dobrokhotov, S. A. Sergeev, “Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source”, Proc. Steklov Inst. Math., 281 (2013), 161–178
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
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”, Russ. J. Math. Phys., 20:4 (2013), 389–401