New exact solitary-wave solutions for the K(2,2,1) and K(3,3,1) equations

Zhu, Yaping; Tong, Kang; Chaolu, Temuer

doi:10.1016/j.chaos.2006.01.090

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…The classic nonlinear dispersive Kðm; nÞ equation first introduced by Rosenau and Hymann (1993) and for certain values of m and n, Kðm; nÞ equation has solitary waves which are compactly supported. Recently, large number of methods were suggested to study the nonlinear dispersive Kðm; nÞ equations, such as Adomian method (Wazwaz, 2002(Wazwaz, , 2003(Wazwaz, , 2004Zhu et al, 2007), Exp-function method (He and Wu, 2006a), variational iteration method (He and Wu, 2006b;Wazwaz, 2007;Tian and Yin, 2007), variational method (He, 2006a, b) and HPM (He, 2005a, b;Odibat, 2007). There are also many effective and convenient methods for solving these type equations (Inç, 2006;Zhu and Lu, 2006;Zhu and Gao, 2006;Tian and Yin, 2005).…”

Section: Introductionmentioning

confidence: 99%

Homotopy perturbation method for the nonlinear dispersive K(m, n, 1) equations with fractional time derivatives

Koçak

Öziş²,

Yıldırım³

2010

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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PurposeThis paper aims to apply He's homotopy perturbation method (HPM) to obtain solitary solutions for the nonlinear dispersive equations with fractional time derivatives.Design/methodology/approachThe authors choose as an example the nonlinear dispersive and equations with fractional time derivatives to illustrate the validity and the advantages of the proposed method.FindingsThe paper extends the application of the HPM to obtain analytic and approximate solutions to the nonlinear dispersive equations with fractional time derivatives.Originality/valueThis paper extends the HPM to the equation with fractional time derivative.

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Section: Introductionmentioning

confidence: 99%

Homotopy perturbation method for the nonlinear dispersive K(m, n, 1) equations with fractional time derivatives

Koçak

Öziş²,

Yıldırım³

2010

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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“…Zhu et al (2007) obtained some numerical solutions of the nonlinear dispersive K(m, p, 1) equation by using Adomian decomposition method. Also Inc (2008) used Variational iteration method for solving the nonlinear dispersive K(m, p, 1) equations.…”

Section: Introductionmentioning

confidence: 99%

Exact solitary-wave solutions for the nonlinear dispersive K(2,2,1) and K(3,3,1) equations

Mohyud‐Din

Yıldırım

2010

Journal of King Saud University - Science

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We implemented homotopy analysis method for approximating the solution to the nonlinear dispersive K(m,p,1) type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the homotopy analysis series.

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“…where a, b are constants, while l, m and n are positive integers. Zhu et al [15] applied the decomposition method and symbolic computation system to develop some new exact solitary wave solutions for the K(2, 2, 1) equation 5) and the K(3, 3, 1) equation…”

Section: Introductionmentioning

confidence: 99%