Cnoidal wave, snoidal wave, and soliton solutions of the D(m,n) equation

被引：7

作者：

Ebadi G. ^{[1
]}

Krishnan E.V. ^{[2
]}

Johnson S. ^{[3
,4
]}

Biswas A. ^{[4
]}

机构：

[1] Faculty of Mathematical Sciences, University of Tabriz, Tabriz

[2] Department of Mathematics and Statistics, Sultan Qaboos University, P.O.Box 36, Al-Khod 123, Muscat

[3] Lake Forest High School, 5407 Killens Pond Road, Felton, 19943, DE

[4] Department of Mathematical Sciences, Delaware State University, Dover, 19901-2277, DE

来源：

Arabian Journal of Mathematics | 2013年 / 2卷 / 1期

关键词：

37K10; 35Q51; 35Q55;

D O I：

10.1007/s40065-012-0056-8

中图分类号：

学科分类号：

摘要：

This paper studies the D(m,n) equation, which is the generalized version of the Drinfeld–Sokolov equation. The traveling wave hypothesis and exp-function method are applied to integrate this equation. The mapping method and the Weierstrass elliptic function method also display an additional set of solutions. The kink, soliton, shock waves, singular soliton solution, cnoidal and snoidal wave solutions are all obtained by these varieties of integration tools. [Figure not available: see fulltext.] © 2012, The Author(s).

引用

页码：19 / 31

页数：12

共 14 条

[1]

Afrouzi G.A., VahidiJ.

[2]

Saeidy M., Numerical solutions of generalized Drinfeld-Sokolovequations using the homotopy analysis method, Int. J. Nonlinear Sci., 9, 2, pp. 165-170, (2010)

[3]

Bekir A., New exact traveling wave solutions for regularized long-wave, Phi-Four and Drinfeld-Sokolov equations, Int. J. Nonlinear Sci., 6, 1, pp. 46-52, (2008)

[4]

Biswas A., Triki H., 1-soliton solution of the D(m,n) equation with generalized evolution, Appl. Math. Comput., 217, 21, pp. 8490-8496, (2011)

[5]

Kara A.H., An analysis of the symmetries and conservation laws of the class of Zakharov–Kuznetsov equations, Math. Comput. Appl., 15, 4, pp. 658-664, (2010)

[6]

Krishnan E.V., Biswas A., Solutions of the Zakharov–Kuznetsov equation with higher order nonlinearity by mapping and ansatz method, Phys. Wave Phenom., 18, 4, pp. 256-261, (2010)

[7]

Krishnan E.V., Peng Y., A new solitary wave solution for the new Hamiltonian amplitude equation, J. Phys. Soc. Japan., 74, pp. 896-897, (2005)

[8]

Krishnan E.V., Peng Y., Squared Jacobian elliptic function solutions for the (2+1)-D Korteweg de Vries equation, Adv. Theoret. Appl. Math., 1, pp. 9-25, (2006)

[9]

Krishnan E.V., Peng Y., Exact solutions to the combined KdV–mKdV equation by the extended mapping method, Phys. Scripta., 73, pp. 405-409, (2006)

[10]

Wazwaz A.M., Exact and explicit traveling wave solutions for the nonlinear Drinfeld–Sokolov system, Commun. Nonlinear Sci. Numer. Simul., 11, 3, pp. 311-325, (2006)

← 1 2 →