The exp-function method for new exact solutions of the nonlinear partial differential equations

2011 ◽  
Vol 6 (29) ◽  
Author(s):  
Hasibun Naher
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
New Exact Solutions

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

scholarly journals New exact solutions of fractional Hirota-Satsuma coupled Korteweg-de Vries equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1173-1176 ◽  
Author(s):  
Lian-Xiang Cui ◽  
Li-Mei Yan ◽  
Yan-Qin Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Function Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Complex Transform ◽  
New Exact Solutions ◽  
Non Linear ◽  
De Vries

An improved extended tg-function method, which combines the fractional complex transform and the extended tanh-function method, is applied to find exact solutions of non-linear fractional partial differential equations. Generalized Hirota-Satsuma coupled Korteweg-de Vries equations are used as an example to elucidate the effectiveness and simplicity of the method.

scholarly journals Exp-Function Method for Solving Fractional Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bin Zheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Function Method ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
New Exact Solutions ◽  
Complex Transformation ◽  
Liouville Derivative

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

scholarly journals A Family of Novel Exact Solutions to2+1-Dimensional KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhen Wang ◽  
Li Zou ◽  
Zhi Zong ◽  
Hongde Qin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Lax Pair ◽  
Partial Differential ◽  
Independent Variables ◽  
New Exact Solutions

We introduce two subequations with different independent variables for constructing exact solutions to nonlinear partial differential equations. In order to illustrate the efficiency and usefulness, we apply this method to2+1-dimensional KdV equation, which was first derived by Boiti et al. (1986) using the idea of the weak Lax pair. As a result, we obtained many new exact solutions.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

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