EXACT EXPLICIT TRAVELING WAVE SOLUTIONS FOR A NEW COUPLED ZK SYSTEM

Minzhi Wei; Shengqiang Tang

doi:10.11948/2011018

2011 Volume 1 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2011 > 1(2): 267-277

Next Article Previous Article

Minzhi Wei, Shengqiang Tang. EXACT EXPLICIT TRAVELING WAVE SOLUTIONS FOR A NEW COUPLED ZK SYSTEM[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 267-277. doi: 10.11948/2011018

Citation:

Minzhi Wei, Shengqiang Tang. EXACT EXPLICIT TRAVELING WAVE SOLUTIONS FOR A NEW COUPLED ZK SYSTEM[J]. Journal of Applied Analysis & Computation, 2011, 1(2): 267-277. doi: 10.11948/2011018

EXACT EXPLICIT TRAVELING WAVE SOLUTIONS FOR A NEW COUPLED ZK SYSTEM

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, P. R. China

Fund Project:

Abstract

Abstract

The extended tanh-coth method and sech method are used to construct exact solutions of a new coupled ZK system. Traveling wave solutions are determined, which include solitary wave and periodic wave solutions.
- the extended tanh-coth method /
- the sech method /
- solitary wave /
- periodic wave /
- coupled ZK equation
MSC: 74J35;35Q51

FullText(HTML)

References

[1]	MJ. Ablowitz and PA. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, Cambridge:Cambridge University Press, 1991. Google Scholar
[2]	B. Feng, B. Malomed and T. Kawahara, Cylindrical solitary pulses in a twodimensional stabilized Kuramoto-Sivashinsky system, Phys. D., 175(2003), 127-38. Google Scholar
[3]	E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277(2000), 212-218. Google Scholar
[4]	B. Li, Y. Chen and H. Zhang, Exact travelling wave solutions for a generalized Zakharov-Kuznetsov equation, Appl. Math. Comput., 146(2003), 653-666. Google Scholar
[5]	S. Munro and EJ. Parkes, The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions, J. Plasma. Phys., 62(1999), 305-317. Google Scholar
[6]	S. Munro and EJ. Parkes, Stability of solitary-wave solutions to a modified ZakharovCKuznetsov equation, J. Plasma. Phys., 64(2000), 411-426. Google Scholar
[7]	W. Malfliet, The tanh method:I. Exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54(1996), 563-568. Google Scholar
[8]	W. Malfliet and W. Hereman, The tanh method:Ⅱ. Perturbation technique for conservative systems, Phys. Scr., 54(1996), 569-575. Google Scholar
[9]	ZY. Qin, A finite-dimensional integrable system related to a new coupled KdV hierarchy, Phys. Lett. A, 355(2006), 452-459. Google Scholar
[10]	BK. Shivamoggi, The Painlev analysis of the Zakharov-Kuznetsov equation, Phys. Scr., 42(1990), 641-642. Google Scholar
[11]	H. Schamel, A modified Kortweg-de Vries equation for ion acoustic waves due to resonant electrons, J. Plasma. Phys., 9(1973), 377-387. Google Scholar
[12]	S. Tang, Y. Xiao and Z. Wang, Travelling wave solutions for a class of nonlinear fourth order variant of a generalized Camassa-Holm equation, Appl. Math. Comput., 210(2009), 39-47. Google Scholar
[13]	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., 10(2005), 597-606. Google Scholar
[14]	A.M. Wazwaz, The extended tanh method for the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms, Commun. Nonlinear. Sci. Numer. Simul., 13(2008), 1039-1047. Google Scholar
[15]	A.M. Wazwaz, Completely integrable coupled KdV and coupled KP systems, Commun. Nonlinear. Sci. Numer. Simulat., 15(2010), 2828-2835. Google Scholar
[16]	A.M. Wazwaz, Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation, Appl. Math. Comput., 134(2003), 487-500. Google Scholar
[17]	A.M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math. Comput. Model., 40(2004), 499-508. Google Scholar
[18]	D. S. Wang and H.Q. Zhang, Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation, Chaos, Solitons and Fractals, 25(2005), 601-610. Google Scholar
[19]	D. S. Wang and H. Li, Single and multi-solitary wave solutions to a class of nonlinear evolution equations, J. Math. Anal. Appl., 343(2008), 273-298. Google Scholar
[20]	D. S. Wang, D. J. Zhang and J. Yang, Integrable properties of the general coupled nonlinear Schrödinger equations, J. Math. Phys., 51(2010), 023510. Google Scholar
[21]	J. Wu, New explicit travelling wave solutions for three nonlinear evolution equations, Appl. Math. Comput., 217(2010), 1764-1770. Google Scholar
[22]	VE. Zakharov and EA. Kuznetsov, On three-dimensional solitons, Sov. Phys., 39(1974), 285-288. Google Scholar