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

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References

  1. J. J. Stoker, Water Waves: The Mathematical Theory with Applications (John Wiley & Sons, New York, 1992).

    Book  MATH  Google Scholar 

  2. E. N. Pelinovskii, Hydrodynamics of Tsunami Waves (Institute of Applied Physics, Russian Academy of Sciences, Nizhni Novgorod, 1996) [in Russian].

    Google Scholar 

  3. C. C. Mei, The Applied Dynamics of Ocean Surface Waves (JohnWiley & Sons, New York, 1983).

    MATH  Google Scholar 

  4. 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].

    Google Scholar 

  5. S. Yu. Dobrokhotov, Dokl. Akad. Nauk SSSR 269 (1), 76–80 (1983) [Soviet Phys. Dokl. 28, 229–231 (1983)].

    MathSciNet  Google Scholar 

  6. S. Yu. Dobrokhotov and P. N. Zhevandrov, Funktsional. Anal. Prilozhen. 19 (4), 43–54 (1985) [Functional Anal. Appl. 19 (4), 285–295 (1985)].

    MathSciNet  Google Scholar 

  7. 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)].

    Google Scholar 

  8. V. P. Maslov, Uspekhi Mat. Nauk 38 (6 (234)), 3–36 (1983) [Russian Math. Surveys 38 (6), 1–42 (1983)].

    MathSciNet  Google Scholar 

  9. M. V. Berry, New J. Phys. 7 (129), 1–18 (2005).

    MathSciNet  Google Scholar 

  10. M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2087), 3055–3071 (2007).

    Article  MathSciNet  Google Scholar 

  11. V. P. Maslov, Perturbation Theory and Asymptotic Methods (Izd. Moskov. Univ., Moscow, 1965) [in Russian].

    Google Scholar 

  12. V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation for the Equations of Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

  13. S. Yu. Dobrokhotov, A. I. Shafarevich, and B. Tirozzi, Russ. J. Math. Phys. 15 (2), 192–221 (2008).

    Article  MathSciNet  Google Scholar 

  14. S. Yu. Dobrokhotov, R. V. Nekrasov, and B. Tirozzi, J. Engng. Math. 69 (2-3), 225–242 (2011).

    Article  Google Scholar 

  15. 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)].

    Google Scholar 

  16. S. Yu. Dobrokhotov, S. A. Sergeev, and B. Tirozzi, Russ. J. Math. Phys. 20 (2), 155–171 (2013).

    Article  MathSciNet  Google Scholar 

  17. S. Ya. Sekerzh-Zenkovich, Russ. J. Math. Phys. 16 (2), 315–322 (2009).

    Article  MathSciNet  Google Scholar 

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Correspondence to S. Yu. Dobrokhotov.

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Original Russian Text © S. Yu. Dobrokhotov, V. E. Nazaikinskii, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 6, pp. 936–942.

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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

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