A generalized exp-function method for multiwave solutions of sine-Gordon equation

Zhang, Sheng; Wang, Jian; Peng, Au-Xue; Cai, Bin

doi:10.1007/s12043-013-0613-5

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…The existing researches show that the exp-function method and its improvements are available for many nonlinear PDEs, such as those in [2][3][4][5][6][7][8][9]. This is due to the exp-function method possesses a more general ansätz [10]: …”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of Three Nonlinear Systems via Exp-Function Method

Zhang¹,

Wang²

2017

dtcse

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Abstract. In this paper, the exp-function method is used to exactly solve three nonlinear partial differential systems, i.e., the (4+1)-dimensional Fokas equation, the variable-coefficient Burger's equation and the variable-coefficient Benjamin-Bona-Mahony (BBM) equation. As a result, three exact solutions are obtained. It is shown that the exp-function method is a useful mathematical tool for solving some other high-dimensional nonlinear partial differential equations (PDEs) and variable-coefficient nonlinear PDEs.

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Section: Introductionmentioning

confidence: 99%

Exact Solutions of Three Nonlinear Systems via Exp-Function Method

Zhang¹,

Wang²

2017

dtcse

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“…In recent years, many researchers have shown great interest in the search for exact solutions to nonlinear fPDEs. At present, several methods for finding the exact solutions of fPDEs have been presented, for example, the Adomian decomposition method [3][4][5][6], variational iteration method [7][8][9], homotopy perturbation method [10][11][12][13], homotopy analysis method [14,15], differential transform method [16], spectral methods [17,18], discontinuous Galerkin method [19], Kansa method [20], fractional subequation method [21], generalized fractional subequation method [22], fractional projective Riccati expansion method [23], exp-function method [24,25], ( / )-expansion method [26][27][28], functional variable method [29,30], and first integral method [31,32].…”

Section: Introductionmentioning

confidence: 99%

“…Figures 1-6. It can be observed from (15)-(24) andFigures 1-6 that triangular periodic solution, bell-shaped solitary wave solution, kink-shaped solitary wave solution, and Jacobi elliptic function solution of the time fractional simplified MCH are obtained. When = 1, (9) becomes (10), namely, simplified MCH equation, and = − , obviously, (10) still have triangular periodic solution, bell-shaped solitary wave solution, kinkshaped solitary wave solution, and Jacobi elliptic function four types of solutions.…”

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confidence: 99%

A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

Guo

Zhang

et al. 2017

Mathematical Problems in Engineering

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A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

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“…Among the existing methods, the exp-function method [1] proposed by He and Wu in 2006 is a simple and direct method for nonlinear PDEs. More importantly, the exp-function method and its improvements are available for many PDEs such as those in [9][10][11][12][13][14][15][16], this is due to the method possesses a more general ansätz [17]: …”

Section: Introductionmentioning

confidence: 99%