One method for finding exact solutions of nonlinear differential equations
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In this article, a method for finding exact solutions of nonlinear differential equations is considered and modifications of the method are discussed, showing that the method is one of the most effective approaches for solving nonlinear problems.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2012-06-01 and is currently open access. It has received 569 citations till now. The article focuses on the topics: Exact differential equation & Integrating factor.read more
Citations
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Method for finding highly dispersive optical solitons of nonlinear differential equations
TL;DR: In this paper, a method for finding exact solutions in the form of a solitary wave for nonlinear differential equations is presented, which has significant advantages over other approaches of this type.
Journal ArticleDOI
A generalized model for description of propagation pulses in optical fiber
TL;DR: In this paper, the Schrodinger equation with arbitrary power of nonlinearity is considered and the influence of the non-linearity degree on the structure of periodic and solitary waves is studied.
Journal ArticleDOI
Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations
TL;DR: By using the Kudryashov method, new conformable fractional derivative is applied for converting fractional coupled nonlinear Schrodinger equations into the ordinary differential equations and new traveling wave solutions are extracted.
Journal ArticleDOI
Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations
TL;DR: A new approach for finding solitary wave solutions of high-order nonlinear differential equations of perturbed Schrodinger equations of the fourth, sixth, eighth, tenth and twelfth orders is presented.
Journal ArticleDOI
New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method
Kamyar Hosseini,Reza Ansari +1 more
TL;DR: In this paper, the modified Kudryashov method was used to derive exact solutions for nonlinear Boussinesq equations with conformable time-fractional derivative.
References
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Exp-function method for nonlinear wave equations
Ji-Huan He,Xu-Hong Wu +1 more
TL;DR: In this article, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations, and the modified KdV equation and Dodd-Bullough-Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.
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The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
TL;DR: The (G'/G)-expansion method is firstly proposed in this paper, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equations, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained when the parameters are taken as special values.
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.
Journal ArticleDOI
An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations
E.J. Parkes,Brian R. Duffy +1 more
TL;DR: In this article, the tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described, and a Mathematica package ATFM is presented to deal with the tedious algebra and outputs directly the required solutions.
Journal ArticleDOI
Simplest equation method to look for exact solutions of nonlinear differential equations
TL;DR: In this paper, a new method is presented to look for exact solutions of nonlinear differential equations by using the general solutions of the simplest nonlinear equations and taking into consideration all possible singularities of equation studied.
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