New exact solutions for fractional Sine-Gordon equation by using the new version of generalized F-expansion method

2016 ◽  
Author(s):  
Yusuf Pandir ◽  
Hasan Huseyin Duzgun
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Expansion Method ◽  
Sine Gordon Equation ◽  
New Exact Solutions

scholarly journals Some New Exact Solutions of (1+2)-Dimensional Sine-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wei-Xiong Chen ◽  
Ji Lin
Keyword(s):  
Gordon Equation ◽  
Direct Method ◽  
Wave Interaction ◽  
Expansion Method ◽  
Periodic Wave ◽  
Sine Gordon Equation ◽  
Interaction Solutions ◽  
New Exact Solutions ◽  
Propagation Properties ◽  
A Direct Method

We use a generalized tanh function expansion method and a direct method to study the analytical solutions of the (1+2)-dimensional sine Gordon (2DsG) equation. We obtain some new interaction solutions among solitary waves and periodic waves, such as the kink-periodic wave interaction solution, two-periodic solitoff solution, and two-toothed-solitoff solution. We also investigate the propagation properties of these solutions.

scholarly journals Sine-Gordon Expansion Method for Exact Solutions to Conformable Time Fractional Equations in RLW-Class

2017 ◽  
Author(s):  
Alper Korkmaz ◽  
Ozlem Ersoy Hepson ◽  
Kamyar Hosseini ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Expansion Method ◽  
Algebraic Equations ◽  
Sine Gordon Equation ◽  
Fractional Equations ◽  
Polynomial Type ◽  
Long Wave ◽  
Previous Step ◽  
Homogeneous Balance

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

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