EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 7 / No 2 (2012) Math. Model. Nat. Phenom., 7 2 (2012) 113-130 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 2, 2012
Solitary waves
Page(s) 113 - 130
DOI https://doi.org/10.1051/mmnp/20127210
Published online 29 February 2012
  1. M.J. Ablowitz, H. Segur. Solitons and the Inverse Scattering Transform. SIAM, Philadelphia, 1981. [Google Scholar]
  2. J. Apel, L.A. Ostrovsky, Y.A. Stepanyants, J.F. Lynch. Internal solitons in the ocean and their effect on underwater sound, J. Acoust. Soc. Am., 121 (2007), No. 2, 695–722. [CrossRef] [PubMed] [Google Scholar]
  3. Yu. Berezin. Modelling Nonlinear Wave Processes. VNU Science Press, 1987. [Google Scholar]
  4. M. Dehghan, F. Fakhar-Izadi. The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves, Math. Comp. Modelling, 53 (2011), 1865–1877. [CrossRef] [Google Scholar]
  5. V.M. Galkin, Yu.A. Stepanyants. On the existence of stationary solitary waves in a rotating fluid, J. Appl. Maths. Mechs., 55 (1991), No. 6, 939–943 (English translation of the Russian journal “Prikladnaya Matematika i Mekhanika”). [CrossRef] [Google Scholar]
  6. O.A. Gilman, R. Grimshaw, Yu.A. Stepanyants. Approximate analytical and numerical solutions of the stationary Ostrovsky equation, Stud. Appl. Math., 95 (1995), No. 1, 115–126. [MathSciNet] [Google Scholar]
  7. O.A. Gilman, R. Grimshaw, Yu.A. Stepanyants. Dynamics of internal solitary waves in a rotating fluid, Dynamics. Atmos. and Oceans, 23 (1996), No. 1–4, 403–411. [CrossRef] [Google Scholar]
  8. R. Grimshaw, J.-M. He, L.A. Ostrovsky. Terminal damping of a solitary wave due to radiation in rotational systems, Stud. Appl. Math., 101 (1998), 197–210. [CrossRef] [MathSciNet] [Google Scholar]
  9. R. Grimshaw, L.A. Ostrovsky, V.I. Shrira, Yu.A. Stepanyants. Long nonlinear surface and internal gravity waves in a rotating ocean, Surveys in Geophys., 19 (1998), 289–338. [CrossRef] [Google Scholar]
  10. R. Grimshaw, K. Helfrich. Long-time solutions of the Ostrovsky equation, Stud. Appl. Math., 121 (2008), No. 1, 71–88. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Holloway, E. Pelinovsky, T. Talipova. A generalised Korteweg-de Vries model of internal tide transformation in the coastal zone, J. Geophys. Res. 104 (1999), No. 18, 333–350. [NASA ADS] [CrossRef] [Google Scholar]
  12. A.I. Leonov. The effect of the Earth’s rotation on the propagation of weak nonlinear surface and internal long oceanic waves, Ann. New York Acad. Sci., 373 (1981), 150–159. [CrossRef] [Google Scholar]
  13. M.A. Obregon, Yu.A. Stepanyants. Oblique magneto-acoustic solitons in rotating plasma, Phys. Lett. A, 249, (1998), No. 4, 315–323. [Google Scholar]
  14. L.A. Ostrovsky. Nonlinear internal waves in a rotating ocean, Oceanology, 18 (1978), 119–125. (English translation of the Russian journal “Okeanologiya”). [Google Scholar]
  15. L.A. Ostrovsky, Yu.A. Stepanyants. Nonlinear surface and internal waves in rotating fluids. In : “Nonlinear Waves 3”, Proc. 1989 Gorky School on Nonlinear Waves, (1990), 106–128. Eds. A.V. Gaponov-Grekhov, M.I. Rabinovich and J. Engelbrecht, Springer-Verlag, Berlin–Heidelberg. [Google Scholar]
  16. L.A. Ostrovsky, Yu.A. Stepanyants. Internal solitons in laboratory experiments : Comparison with theoretical models, Chaos, 15, (2005) 037111, 28 p. [Google Scholar]
  17. D.E. Pelinovsky, Yu.A. Stepanyants. Convergence of Petviashvili’s iteration method for numerical approximation of stationary solutions of nonlinear wave equations, SIAM J. Numerical Analysis, 42, (2004), 1110–1127. [Google Scholar]
  18. V.I. Petviashvili, O.V. Pokhotelov. Solitary Waves in Plasmas and in the Atmosphere. Gordon and Breach, Philadelphia, 1992. [Google Scholar]
  19. Yu.A. Stepanyants. On stationary solutions of the reduced Ostrovsky equation : Periodic waves, compactons and compound solitons, Chaos, Solitons and Fractals, 28, (2006), 193–204. [CrossRef] [MathSciNet] [Google Scholar]
  20. Yu.A. Stepanyants, I.K. Ten, H. Tomita. Lump solutions of 2D generalised Gardner equation. In : “Nonlinear Science and Complexity”, Proc. of the Conference, Beijing, China, 7–12 August 2006, 264–271. Eds. A.C.J. Luo, L. Dai and H.R. Hamidzadeh, World Scientific, 2006. [Google Scholar]
  21. V.O. Vakhnenko. High-frequency soliton-like waves in a relaxing medium, J. Math. Phys., 40, (1999), 2011–2020. [CrossRef] [MathSciNet] [Google Scholar]
  22. G.B. Whitham. Linear and Nonlinear Waves. John Wiley & Sons, 1974. [Google Scholar]
  23. T. Yaguchi, T. Matsuo, M. Sugihara. Conservative numerical schemes for the Ostrovsky equation, J. Comp. Appl. Maths., 234, (2010), 1036–1048. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.