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2007 | 5 | 3 | 351-366
Tytuł artykułu

Compacton and periodic wave solutions of the non-linear dispersive Zakharov-Kuznetsov equation

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, the nonlinear dispersive Zakharov-Kuznetsov equation is solved by using the sine-cosine method. As a result, compactons, periodic, and singular periodic wave solutions are found.
Wydawca

Czasopismo
Rocznik
Tom
5
Numer
3
Strony
351-366
Opis fizyczny
Daty
wydano
2007-09-01
online
2007-04-28
Twórcy
Bibliografia
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  • [7] A.M. Wazwaz: “Special types of the nonlinear dispersive Zakharov-Kuznetsov equations with compactons, solitons, and periodic solutions”, Int. J. Computer Math., Vol. 81, (2004), pp. 1107–1119. http://dx.doi.org/10.1080/00207160410001684253[Crossref]
  • [8] A.M. Wazwaz: “Nonlinear dispersive special type of the Zakharov-Kuznetsov equation ZK(n,n) with compact and noncompact structures”, Appl. Math. Comput., Vol. 161, (2005), pp. 577–590. http://dx.doi.org/10.1016/j.amc.2003.12.050[Crossref]
  • [9] A.M. Wazwaz: “Exact solutions with solitons and periodic structures for the Zakharov-Kuznetsov (ZK) equation and its modified form”, Commun. Nonlinear Sci. Numer. Simul., Vol. 10, (2005), pp. 597–606. http://dx.doi.org/10.1016/j.cnsns.2004.03.001[WoS][Crossref]
  • [10] A.M. Wazwaz: “Explicit travelling wave solutions of variants of the K(n, n) and the ZK(n, n) equations with compact and noncompact structures”, Appl. Math. Comput., Vol. 173, (2006), pp. 213–230. http://dx.doi.org/10.1016/j.amc.2005.02.050[Crossref]
  • [11] M.S. Ismail and T. Taha: “A numerical study of compactons”, Math. Comput. Simul., Vol. 47, (1998), pp. 519–530. http://dx.doi.org/10.1016/S0378-4754(98)00132-3[Crossref]
  • [12] A. Ludu and J.P. Draayer: “Patterns on liquid surfaces: cnoidal waves, compactons and scaling”, Physica D, Vol. 123, (1998), pp. 82–91. http://dx.doi.org/10.1016/S0167-2789(98)00113-4[Crossref]
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  • [15] S. Monro and E.J. Parkes: “The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions”, J. Plasma Phys., Vol. 62, (1999), pp. 305–317. http://dx.doi.org/10.1017/S0022377899007874[Crossref]
  • [16] S. Monro and E.J. Parkes: “Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation”, J. Plasma Phys., Vol. 64, (2000), pp. 411–426.
  • [17] Z. Yan: “Modified nonlinearly dispersive mK(m,n,k) equations: I. New compacton solutions and solitary pattern solutions”, Comp. Phys. Commun., Vol. 152, (2003), pp. 25–33. http://dx.doi.org/10.1016/S0010-4655(02)00794-4[Crossref]
  • [18] A.M. Wazwaz: “General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces”, Math. Comput. Simul., Vol. 59, (2002), pp. 519–531. http://dx.doi.org/10.1016/S0378-4754(01)00439-6[Crossref]
  • [19] P. Bracken: “Specific solutions of the generalized Korteweg-de Vries equation with possible physical applications”, Cent. Eur. J. Phys, Vol. 3, (2005), pp. 127–138. http://dx.doi.org/10.2478/BF02476511[Crossref]
  • [20] Z. Yan: “New families of solitons with compact support for Boussinesq-like B(m,n) equations with fully nonlinear dispersion”, Chaos, Solitons and Fractals, Vol. 14, (2002), pp. 1151–1158. http://dx.doi.org/10.1016/S0960-0779(02)00062-0[Crossref]
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  • [23] A.M. Wazwaz: Partial Differential Equations: Methods and Applications, Balkema Publishers, The Netherlands, 2002.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-007-0020-y
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