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Asymptotic representation of surface waves in the form of two traveling burgers waves

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References

  1. P. I. Naumkin and I. A. Shishmarev, “Surface-wave equations,” Dokl. Akad. Nauk SSSR,301, No. 4, 788–793 (1988).

    Google Scholar 

  2. J. Boussinesq, “Theorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de surface au fond,” J. Math. Pures Appl. Ser. 2,17, 55–108 (1872).

    Google Scholar 

  3. L. J. Broer, “Approximate equations for long water waves,” Appl. Sci. Res.,31, 377–395 (1975).

    Google Scholar 

  4. S. Yu. Dobrokhotov, “Nonlocal analogs of the nonlinear Boussinesq equation for surface waves over a rough bottom and their asymptotic solutions,” Dokl. Akad. Nauk SSSR,292, No. 1, 63–67 (1987).

    Google Scholar 

  5. D. J. Kaup, “A higher-order water-wave equation and the method for solving it,” Prog. Theor. Phys.,54, No. 2, 396–408 (1975).

    Google Scholar 

  6. E. A. Zabolotskaya and R. V. Khokhlov, “Quasiplane waves in the nonlinear acoustics of reflected beams,” Akust. Zh.,15, No. 1, 40–47 (1969).

    Google Scholar 

  7. P. I. Naumkin and I. A. Shishmarev, “Equations describing surface waves,” Izv. Akad. Nauk SSSR, Ser. Mat.,54, No. 4, 774–809 (1990).

    Google Scholar 

  8. P. I. Naumkin and I. A. Shishmarev, “Destruction of surface waves,” Differents. Uravn.,28, No. 5, 886–892 (1992).

    Google Scholar 

  9. E. I. Kaikina, “Generalized solution of the Cauchy problem for the system of surface-wave equations in the conservative case,” Mat. Modelirovanie,3, No. 12, 107–114 (1991).

    Google Scholar 

  10. P. I. Naumkin and I. A. Shishmarev, “Large-time asymptotics of solutions to the system of surface-wave equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,55, No. 3, 537–559 (1991).

    Google Scholar 

  11. P. Biler, “Regular decay of solutions of strongly damped nonlinear hyperbolic equations,” Appl. Anal.,32, 277–285 (1989).

    Google Scholar 

  12. P. I. Naumkin and I. A. Shishmarev, “Large-time asymptotic relationship between solutions to various nonlinear equations. I,” Differents. Uravn.,30, No. 5, 873–881 (1994).

    Google Scholar 

  13. M. V. Fedoryuk, Asymptotics: Integrals and Series [in Russian], Nauka, Moscow (1987).

    Google Scholar 

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Chair of General Mathematics, Department of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 25–40, July–September, 1995.

The investigation was partially supported by the the Russian Foundation for Basic Research (Grant No. 93-011-131) and the International Science Foundation (Grant No. NBX300).

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Naumkin, P.I., Shishmarev, I.A. Asymptotic representation of surface waves in the form of two traveling burgers waves. Funct Anal Its Appl 29, 168–179 (1995). https://doi.org/10.1007/BF01077050

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