Journal ArticleDOI
The extended tanh method for abundant solitary wave solutions of nonlinear wave equations
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The extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations that include solitons, kinks and plane periodic solutions.About:
This article is published in Applied Mathematics and Computation.The article was published on 2007-04-01. It has received 218 citations till now. The article focuses on the topics: Soliton & Wave equation.read more
Citations
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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.
Journal ArticleDOI
The extended tanh method and its applications for solving nonlinear physical models
TL;DR: The extended tanh method with a computerized symbolic computation is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics and the obtained solutions include solitons, kinks and plane periodic solutions.
Journal ArticleDOI
The tanh–coth method for solitons and kink solutions for nonlinear parabolic equations
TL;DR: The new tanh–coth approach provides abundant solitons and kink solutions in addition to the existing ones and the power of this manageable method is confirmed.
Journal ArticleDOI
Modified extended tanh-function method and its applications to the Bogoyavlenskii equation
TL;DR: In this paper, exact traveling wave solutions of the Bogoyavlenskii equation using a modified extended tanh-function method were considered. But their method has a broad applicability to many other nonlinear evolution equations in mathematical physics.
Journal ArticleDOI
Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in the stochastic input case
TL;DR: In this article, the Riccati-Bernoulli sub-ODE method was used to construct exact traveling wave solutions for the non-linear Schrodinger equation by the new RBN method.
References
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Journal ArticleDOI
Solitary wave solutions of nonlinear wave equations
TL;DR: In this article, a method for obtaining traveling-wave solutions of nonlinear wave equations that are essentially of a localized nature is proposed based on the fact that most solutions are functions of a hyperbolic tangent.
Journal ArticleDOI
The tanh method: I. Exact solutions of nonlinear evolution and wave equations
Willy Malfliet,Willy Hereman +1 more
TL;DR: In this article, a systemized version of the tanh method is used to solve particular evolution and wave equations, where the boundary conditions are implemented in this expansion, and the associated velocity can then be determined a priori, provided the solution vanishes at infinity.
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.
Journal ArticleDOI
The tanh method for traveling wave solutions of nonlinear equations
TL;DR: The tanh method is employed for traveling wave solutions of nonlinear equations and the study is extended to equations that do not have tanh polynomial solutions.
Journal ArticleDOI
The tanh method: II. Perturbation technique for conservative systems
Willy Malfliet,Willy Hereman +1 more
TL;DR: In this paper, a general wave profile, with a perturbative solitary-wave contribution superposed, was obtained for a particular choice of the parameters, and a comparison with the exact solution was made.
Related Papers (5)
The tanh method: I. Exact solutions of nonlinear evolution and wave equations
Willy Malfliet,Willy Hereman +1 more