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Uspekhi Mat. Nauk, 1989, Volume 44, Issue 1(265), Pages 5–34 (Mi umn1759)  

This article is cited in 24 scientific papers (total in 24 papers)

Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems

L. A. Kalyakin


Full text: PDF file (2075 kB)
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English version:
Russian Mathematical Surveys, 1989, 44:1, 3–42

Bibliographic databases:

UDC: 517.958.530.145.7+517.956.226
MSC: 35Q53, 41A60, 35B40
Received: 28.07.1987

Citation: L. A. Kalyakin, “Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems”, Uspekhi Mat. Nauk, 44:1(265) (1989), 5–34; Russian Math. Surveys, 44:1 (1989), 3–42

Citation in format AMSBIB
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\by L.~A.~Kalyakin
\paper Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems
\jour Uspekhi Mat. Nauk
\yr 1989
\vol 44
\issue 1(265)
\pages 5--34
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\transl
\jour Russian Math. Surveys
\yr 1989
\vol 44
\issue 1
\pages 3--42
\crossref{https://doi.org/10.1070/RM1989v044n01ABEH002013}
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    1. V. P. Maslov, G. A. Omel'yanov, “Rapidly oscillating asymptotic solution of magnetohydrodynamic equations in the Tokamak approximation”, Theoret. and Math. Phys., 92:2 (1992), 879–895  mathnet  crossref  mathscinet  zmath  isi
    2. V. P. Maslov, G. A. Omel'yanov, “Three-scale expansion of the solution of the magnetohydrodynamic equations and the Reynolds equation for a tokamak”, Theoret. and Math. Phys., 98:2 (1994), 202–211  mathnet  crossref  mathscinet  zmath  isi
    3. Guido Schneider, “Validity and Limitation of the Newell-Whitehead Equation”, Math Nachr, 176:1 (1995), 249  crossref  mathscinet  zmath  isi
    4. R D Pierce, C E Wayne, Nonlinearity, 8:5 (1995), 769  crossref  mathscinet  zmath  adsnasa  isi
    5. Guido Schneider, “The Long Wave Limit for a Boussinesq Equation”, SIAM J Appl Math, 58:4 (1998), 1237  crossref  mathscinet  zmath  isi
    6. Guido Schneider, “Approximation of the Korteweg–de Vries Equation by the Nonlinear Schrödinger Equation”, Journal of Differential Equations, 147:2 (1998), 333  crossref
    7. L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Guido Schneider, C.Eugene Wayne, “Kawahara dynamics in dispersive media”, Physica D: Nonlinear Phenomena, 152-153 (2001), 384  crossref
    9. S. G. Glebov, O. M. Kiselev, V. A. Lazarev, “Birth of solitons during passage through local resonance”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S84–S90  mathnet  mathscinet  zmath  elib
    10. Johannes Giannoulis, Alexander Mielke, “The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities”, Nonlinearity, 17:2 (2004), 551  crossref  mathscinet  zmath  isi  elib
    11. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    12. A. Veksler, Y. Zarmi, “Perturbative Analysis of Wave Interaction in Nonlinear Systems”, Theoret. and Math. Phys., 144:2 (2005), 1227–1237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Gérard Iooss, Guillaume James, “Localized waves in nonlinear oscillator chains”, Chaos, 15:1 (2005), 015113  crossref  mathscinet  isi
    14. I.V. Andrianov, J. Awrejcewicz, “Continuous models for 1D discrete media valid for higher-frequency domain”, Physics Letters A, 345:1-3 (2005), 55  crossref  elib
    15. I. V. Andrianov, “Approksimatsii Pade i kontinualizatsiya dlya odnomernoi tsepochki mass”, Matem. modelirovanie, 18:1 (2006), 43–58  mathnet  mathscinet  zmath  elib
    16. A. Krylovas, “Asymptotic Method for Approximation of Resonant Interaction of Nonlinear Multidimensional Hyperbolic Waves”, Math Modelling Anal, 13:1 (2008), 47  crossref
    17. R. Arora, “Asymptotical solutions for a vibrationally relaxing gas”, Mathematical Modelling and Analysis, 14:4 (2009), 423  crossref
    18. Johannes Giannoulis, “Interaction of modulated pulses in scalar multidimensional nonlinear lattices”, Gapa, 89:9 (2010), 1413  crossref
    19. A. Krylovas, R. Kriauziene, “Asymptotical Analysis of Some Coupled Nonlinear Wave Equations”, Math. Modelling & Analysis, 16:1 (2011), 97  crossref
    20. Pius Kirrmann, Guido Schneider, Alexander Mielke, “The validity of modulation equations for extended systems with cubic nonlinearities”, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 122:1-2 (2011), 85  crossref
    21. GUILLAUME JAMES, “NONLINEAR WAVES IN NEWTON'S CRADLE AND THE DISCRETE p-SCHRÖDINGER EQUATION”, Math. Models Methods Appl. Sci, 21:11 (2011), 2335  crossref
    22. T. V. Pavlyuk, A. V. Nesterov, “On the asymptotics of the solution to a singularly perturbed hyperbolic system of equations with several spatial variables in the critical case”, Comput. Math. Math. Phys., 54:3 (2014), 462–473  mathnet  crossref  crossref  isi  elib  elib
    23. O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84  mathnet  crossref  mathscinet  isi  elib
    24. Klein Ch. Saut J.-C., “IST Versus PDE: A Comparative Study”, Hamiltonian Partial Differential Equations and Applications, Fields Institute Communications, ed. Guyenne P. Nicholls D. Sulem C., Springer, 2015, 383–449  crossref  mathscinet  zmath  isi
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