scholarly journals On Backlund transformation of Riccati equation method and its application to nonlinear partial differential equations and differential-difference equations

2020 ◽  
Vol 4 (1) ◽  
pp. 56-62
Author(s):  
Reham Hassan ◽  
◽  
Mustafa El-Agamy ◽  
Mohamed Soror Abdel Latif ◽  
Hamed Nour ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Riccati Equation ◽  
Difference Equations ◽  
Bäcklund Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Backlund Transformation ◽  
Partial Differential

Extended Trial Equation Method for Nonlinear Partial Differential Equations

2015 ◽  
Vol 70 (4) ◽  
pp. 269-279 ◽  
Author(s):  
Khaled A. Gepreel ◽  
Taher A. Nofal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
Partial Differential ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Extended Trial

AbstractThe main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber–Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

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