Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations

Shi-Kuo, Liu; Fu, Zuntao; Liu, Shida; Zhao, Qiang

doi:10.1016/s0375-9601(01)00580-1

Cited by 1,246 publications

(549 citation statements)

References 14 publications

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“…However, there are some reasons to select the Exp-function method over the others: (i) The Exp-function method provides exponential function solutions from which we can construct solitary and periodic wave solutions by setting the parameters as special values. (ii) As mentioned in [40], Jacobi elliptic function method [2] cannot be applied to solve the NLEEs in which the odd and evenorder derivative terms coexist. This observation is also true for tanh-coth function method [3] and F-expansion method [6].…”

Section: Analytic Solutions To the (2 + 1)d-zk Equationmentioning

confidence: 99%

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

Aslan

2010

Applied Mathematics and Computation

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a b s t r a c tIn this paper, the Exp-function method is employed to the Zakharov-Kuznetsov equation as a (2 + 1)-dimensional model for nonlinear Rossby waves. The observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient. The obtained results may be useful for better understanding the properties of two-dimensional coherent structures such as atmospheric blocking events.

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Section: Analytic Solutions To the (2 + 1)d-zk Equationmentioning

confidence: 99%

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

Aslan

2010

Applied Mathematics and Computation

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“…Recently Liu et al [10] used three Jacobi elliptic functions (sn(ξ ), cn(ξ ), and dn(ξ )) to construct exact periodic solutions of some nonlinear evolution equations. The expansion method has been further developed into extended ones and also widely applied by Yan [11], Fan [12], Ye [13], etc.…”

Section: Periodic Jacobi Elliptic Function Expansionmentioning

confidence: 99%

Painlevé Properties And Exact Solutions Of The Generalized Coupled Kdv Equations

Li-Jun

Lin

2005

Zeitschrift Für Naturforschung A

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The generalized coupled Korteweg-de Vries (GCKdV) equations as one case of the four-reduction of the Kadomtsev-Petviashvili (KP) hierarchy are studied in details. The Painlevé properties of the model are proved by using the standard Weiss-Tabor-Carnevale (WTC) method, invariant, and perturbative Painlevé approaches. The meaning of the negative index k = −2 is shown, which is indistinguishable from the index k = −1. Using the standard and nonstandard Painlevé truncation methods and the Jacobi elliptic function expansion approach, some types of new exact solutions are obtained.

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“…In recent years, several methods have been established for investigating nonlinear PDEs to obtain exact solutions. For example, the Hirota's bilinear transformation method [1], the B cklund transformation method [2], the Jacobi elliptic function expansion method [3], the generalized Riccati equation method [4,5], the homogeneous balance method [6], the F-expansion method [7], the Exp-function method [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Some new solutions of the (1+1)-dimensional PDE via the improved (G′/G)-expansion method

Naher¹,

Abdullah²

2014

AIP Conference Proceedings

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Abstract. In this article, an improved '/ G G -expansion method is implemented for the simplified Modified CamassaHolm (MCH) equation involving parameters, with an aim to construct many new traveling wave solutions. In this method, second order linear ordinary differential equation with constant coefficients has been implemented as an auxiliary equation. The generated solutions including solitons and periodic solutions are demonstrated by the hyperbolic function, the trigonometric function and the rational forms. If the parameters take particular values, the solutions become in special functional form. Moreover, it is worth mentioning that, some of our solutions are in good agreement with already published results in the open literature by setting appropriate values of constants, which proves our other solutions. In addition, some of obtained solutions are described in the figures with the aid of commercial software Maple 13.

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Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations

Cited by 1,246 publications

References 14 publications

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

Generalized solitary and periodic wave solutions to a (2+1)-dimensional Zakharov–Kuznetsov equation

Painlevé Properties And Exact Solutions Of The Generalized Coupled Kdv Equations

Some new solutions of the (1+1)-dimensional PDE via the improved (G′/G)-expansion method

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