Warianty tytułu
Języki publikacji
Abstrakty
Under investigation in this paper is a two-dimensional Korteweg de Vries model, which is a spacial extension of the Korteweg de Vries model. An infinite number of nonlocal conservation laws are given which indicate the integrability of this model. Exact soliton solutions are then respectively derived by means of the multiple exp-function method.
Czasopismo
Rocznik
Tom
Strony
27--33
Opis fizyczny
Bibliogr. 20 poz., wykr.
Twórcy
autor
- Department of Mathematical Sciences, Material Science Innovation and Modelling Focus Area, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa, abdullahi.adem@nwu.ac.za
Bibliografia
- [1] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991.
- [2] A. R. Adem, A (2 + 1)-dimensional Korteweg de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws, Internat. J. Modern Phys. B 30 (2016), Article ID 1640001.
- [3] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Appl. Math. Sci. 81, Springer, New York, 1989.
- [4] A. F. Cheviakov, GeM software package for computation of symmetries and conservation laws of differential equations, Comput. Phys. Commun. 176 (2007), 48-61.
- [5] A. F. Cheviakov, Computation of fluxes of conservation laws, J. Engrg. Math. 66 (2010), 153-173.
- [6] A. F. Cheviakov, Symbolic computation of local symmetries of nonlinear and linear partial and ordinary differentia equations, Math. Comput. Sci. 4 (2010), 203-222.
- [7] Y. Chen and Z. Yan, The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations, Chaos Solitons Fractals 29 (2006), 948-964.
- [8] S. A. El-Wakil, A. Elgarayhi and A. Elhanbaly, Exact periodic wave solutions for some nonlinear partial differentia equations, Chaos Solitons Fractals 29 (2006), 1037-1044.
- [9] R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194.
- [10] X. Lü and F. Lin, Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order, Commun. Nonlinear Sci. Numer. Simul. 32 (2016), 241-261.
- [11] W. X. Ma, T. W. Huang and Y. Zhang, A multiple exp-function method for nonlinear differential equations and its application, Phys. Scripta 82 (2010), Article ID 065003.
- [12] W. X. Ma and Z. Zhu, Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm, Appl. Math. Comput. 218 (2012), 11871-11879.
- [13] L. N. Song, Q. Wang, Y. Zheng and H. Q. Zhang, A new extended Riccati equation rational expansion method and its application, Chaos Solitons Fractals 31 (2007), 548-556.
- [14] M. Wang and X. Li, Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation, Chaos Solitons Fractals 24 (2005), 1257-1268.
- [15] M. Wang, Y. Zhou and Z. Li, Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A 216 (1996), 67-65.
- [16] R. Wu and J. Sun, Soliton-like solutions to the GKdV equation by extended mapping method, Chaos Solitons Fractals 31 (2007), 70-74.
- [17] C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A 224 (1996), 77-84.
- [18] P. Yan-Ze, A New (2+1)-dimensional KdV equation and its localized structures, Commun. Theor. Phys. (Beijing) 54 (2010), 863-865.
- [19] E. Yomba, On exact solutions of the coupled Klein-Gordan-Schrödinger and the complex coupled KDV equations using mapping method, Chaos Solitons Fractals 21 (2004), 209-229.
- [20] N. J. Zabusky and M. D. Kruskal, Interaction of "solitons" in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett. 15 (1965), 240-243.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-54ca7e48-c8dd-4917-8357-c6d22791bc1a