scholarly journals A note on new exact solutions for the Kawahara equation using Exp-function method

2010 ◽  
Vol 234 (12) ◽  
pp. 3511-3512 ◽  
Author(s):  
Nikolai A. Kudryashov
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Kawahara Equation ◽  
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.

scholarly journals New Exact Solutions for a Generalized Double Sinh-Gordon Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Gabriel Magalakwe ◽  
Chaudry Masood Khalique
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fluid Dynamics ◽  
Exact Solutions ◽  
Function Method ◽  
Gordon Equation ◽  
Quantum Field ◽  
Integrable Quantum ◽  
New Exact Solutions ◽  
Integrable Quantum Field Theory

We study a generalized double sinh-Gordon equation, which has applications in various fields, such as fluid dynamics, integrable quantum field theory, and kink dynamics. We employ the Exp-function method to obtain new exact solutions for this generalized double sinh-Gordon equation. This method is important as it gives us new solutions of the generalized double sinh-Gordon equation.

Application of the Exp-Functionmethod to the Riccati Equation and New Exact Solutions with Three Arbitrary Functions of Quantum Zakharov Equations

2008 ◽  
Vol 63 (10-11) ◽  
pp. 646-652 ◽  
Author(s):  
Mohamed A Abdou ◽  
Essam M. Abulwafa
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
New Exact Solutions ◽  
Generalized Riccati Equation ◽  
Solitary Solutions

The Exp-function method with the aid of the symbolic computational system is used for constructing generalized solitary solutions of the generalized Riccati equation. Based on the Riccati equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of quantum Zakharov equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics.

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.

New exact solutions of space and time fractional modified Kawahara equation

2020 ◽  
Vol 551 ◽  
pp. 124550 ◽  
Author(s):  
Sevil Çulha Ünal ◽  
Ayşegül Daşcıoğlu ◽  
Dilek Varol Bayram
Keyword(s):  
Exact Solutions ◽  
Kawahara Equation ◽  
Space And Time ◽  
New Exact Solutions

Two New Applications of the Modified Extended Tanh-Function Method

2003 ◽  
Vol 58 (1) ◽  
pp. 39-44 ◽  
Author(s):  
S. A. Elwakil ◽  
S. K. El-labany ◽  
M. A. Zahran ◽  
R. Sabry
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Function Method ◽  
New Exact Solutions ◽  
New Applications

Based on a modified extended tanh-function method and symbolic computation, new exact solutions are found for a soliton breaking equation and coupled kdv system. The obtained solutions include rational, soliton, singular and periodical solutions.

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