References
J. J. Stoker, Water Waves: The Mathematical Theory with Applications (John Wiley & Sons, New York, 1992).
E. N. Pelinovskii, Hydrodynamics of Tsunami Waves (Institute of Applied Physics, Russian Academy of Sciences, Nizhni Novgorod, 1996) [in Russian].
C. C. Mei, The Applied Dynamics of Ocean Surface Waves (JohnWiley & Sons, New York, 1983).
D. A. Indeitsev, N. G. Kuznetsov, O. V. Motygin, and Yu. A. Mochalova, Localization of LinearWaves (Izd. St. Petersburg Gos. Univ., St. Petersburg., 2007) [in Russian].
S. Yu. Dobrokhotov, Dokl. Akad. Nauk SSSR 269 (1), 76–80 (1983) [Soviet Phys. Dokl. 28, 229–231 (1983)].
S. Yu. Dobrokhotov and P. N. Zhevandrov, Funktsional. Anal. Prilozhen. 19 (4), 43–54 (1985) [Functional Anal. Appl. 19 (4), 285–295 (1985)].
S. Yu. Dobrokhotov, P. N. Zhevandrov, and M. V. Kuz’mina, Mat. Zametki 53 (6), 141–148 (1993) [Math. Notes 53 (5–6), 657–660 (1993)].
V. P. Maslov, Uspekhi Mat. Nauk 38 (6 (234)), 3–36 (1983) [Russian Math. Surveys 38 (6), 1–42 (1983)].
M. V. Berry, New J. Phys. 7 (129), 1–18 (2005).
M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2087), 3055–3071 (2007).
V. P. Maslov, Perturbation Theory and Asymptotic Methods (Izd. Moskov. Univ., Moscow, 1965) [in Russian].
V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation for the Equations of Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].
S. Yu. Dobrokhotov, A. I. Shafarevich, and B. Tirozzi, Russ. J. Math. Phys. 15 (2), 192–221 (2008).
S. Yu. Dobrokhotov, R. V. Nekrasov, and B. Tirozzi, J. Engng. Math. 69 (2-3), 225–242 (2011).
S. Yu. Dobrokhotov, V. E. Nazaikinskii, and A. I. Shafarevich, Dokl. Ross. Akad. Nauk [Dokl. Math.] 466 (6), 641–644 (2016) [Dokl. Math. 93 (1), 99–102 (2016)].
S. Yu. Dobrokhotov, S. A. Sergeev, and B. Tirozzi, Russ. J. Math. Phys. 20 (2), 155–171 (2013).
S. Ya. Sekerzh-Zenkovich, Russ. J. Math. Phys. 16 (2), 315–322 (2009).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S. Yu. Dobrokhotov, V. E. Nazaikinskii, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 6, pp. 936–942.
Rights and permissions
About this article
Cite this article
Dobrokhotov, S.Y., Nazaikinskii, V.E. Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. Math Notes 101, 1053–1060 (2017). https://doi.org/10.1134/S0001434617050339
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434617050339