A sine-cosine method for handlingnonlinear wave equations
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TLDR
A sine-cosine method is used for obtaining traveling wave solutions for nonlinear wave equations with minimal algebra and is applied to selected physical models to illustrate the usage of the main results.About:
This article is published in Mathematical and Computer Modelling.The article was published on 2004-09-01 and is currently open access. It has received 688 citations till now. The article focuses on the topics: Wave equation.read more
Citations
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A multiple exp-function method for nonlinear differential equations and its application
TL;DR: In this article, a multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed, which is oriented towards ease of use and capability of computer algebra systems.
Journal ArticleDOI
A multiple exp-function method for nonlinear differential equations and its application
TL;DR: In this paper, a multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations is proposed, oriented towards the ease of use and capability of computer algebra systems.
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Application of hes homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations
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Application of the (G′G)-expansion method for nonlinear evolution equations
TL;DR: In this paper, the authors established abundant travelling wave solutions for some nonlinear evolution equations, expressed by the hyperbolic functions, the trigonometric functions, and the rational functions.
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Exact solutions for nonlinear evolution equations using Exp-function method
Ahmet Bekir,Ahmet Boz +1 more
TL;DR: In this article, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations, including the Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations.
References
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A review of the decomposition method in applied mathematics
TL;DR: The decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions, closure approximations, perturbation theory, or restrictive assumptions on stochasticitiy as mentioned in this paper.
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Compactons: Solitons with finite wavelength.
TL;DR: The behavior and the stability of these compactons is very similar to that observed in completely integrable systems.
Book
Partial differential equations : methods and applications
TL;DR: In this article, the newly developed Adomian decomposition method along with its modification and some traditional techniques are described and revised, and the new method is described. But the method is not discussed.
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The Modified Korteweg-de Vries Equation
TL;DR: In this paper, it was shown that the N -soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the k-means soliton collision.