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2005 | 3 | 1 | 127-138
Tytuł artykułu

Specific solutions of the generalized Korteweg-de Vries equation with possible physical applications

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Solutions for a type of generalized Korteweg-de Vries equation which should have physical impact will be determined here. These types of solutions should have applications in the study of intrinsic localized modes optical waveguide arrays and fluid dynamics. It is shown that trigonometric and hyperbolic solutions can be obtained by matching powers and coefficients of the independent terms in the equation after the assumed solution has been substituted. As well, solutions to the equation in terms of more complicated Jacobe elliptic functions are determined.
Słowa kluczowe
Wydawca

Czasopismo
Rocznik
Tom
3
Numer
1
Strony
127-138
Opis fizyczny
Daty
wydano
2005-03-01
online
2005-03-01
Twórcy
autor
  • Department of Mathematics, University of Texas, 1201 W. University Dr., 78541-2999, Edinburg, USA, bracken@panam.edu
Bibliografia
  • [1] S. Dusuel, P. Michaux and M. Remoissenet: “From kinks to compactonlike kinks”,Phys. Rev. E,Vol. 57, (1998),pp. 2320–2326. http://dx.doi.org/10.1103/PhysRevE.57.2320[Crossref]
  • [2] P.T. Dinda and M. Remoissenet: “Breather compactons in nonlinear Klein-Gordon systems”,Phys. Rev. E,Vol. 60, (1999),pp. 6218–6121. http://dx.doi.org/10.1103/PhysRevE.60.6218[Crossref]
  • [3] P. Rosenau and J.M. Hyman: “Compactons: Solitons with Finite Wavelength”,Phys. Rev. Lett,Vol. 70 (1993),pp. 564–567. http://dx.doi.org/10.1103/PhysRevLett.70.564[Crossref]
  • [4] P. Bracken: “Some methods for generating solutions to the Korteweg-de Vries equation”,Physica A, Vol. 335, (2004), pp. 70–78. http://dx.doi.org/10.1016/j.physa.2003.11.026[WoS][Crossref]
  • [5] P. Bracken: “Symmetry Properties of the Generalized Korteweg-de Vries Equation And Some Explicit Solutions”,Texas preprint
  • [6] A.M. Wazwaz: “Exact special solutions with solitary patterns for the nonlinear dispersiveK(m, n) equations”,Chaos, Solitons and Fractals,Vol. 13, (2001),pp. 161–170. http://dx.doi.org/10.1016/S0960-0779(00)00248-4[Crossref]
  • [7] A.M. Wazwaz: “New solitary-wave special solutions with compact support for the nonlinear dispersiveK(m, n) equations”,Chaos, Solitons and Fractals,Vol. 13, (2002),pp. 321–330. http://dx.doi.org/10.1016/S0960-0779(00)00249-6[Crossref]
  • [8] C. Yan: “A simple transformation for nonlinear waves”,Physics Letters A,Vol. 224, (1996,pp. 77–84. http://dx.doi.org/10.1016/S0375-9601(96)00770-0[Crossref]
  • [9] Z. Fu, S. Liu and S. Liu: “New transformations and new approach to find exact solutions to nonlinear equations”,Physics Letters A,Vol. 299, (2002),pp. 507–512. http://dx.doi.org/10.1016/S0375-9601(02)00737-5[Crossref]
  • [10] J. Dalibard, J.M. Raimond and J. Zinn-Justin:Fundamental Systems in Quantum Optics, Les Houches, Session LIII, North-Holland, 1992.
  • [11] 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]
  • [12] D.K. Campbell, S. Flach and Y. Kivshar: “Localizing Energy Through Nonlinearity and Discreteness”,Physics Today,Vol. 57, (2004),pp. 43–49.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02476511
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