scholarly journals New Approach of Generalized $\exp ( -\phi ( \xi ) ) $ Expansion Method And Its Application to Som Nonlinear Partial Differential Equations

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Khalil Hasan Yahya ◽  
Zelal. Amin. Moussa
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Partial Differential ◽  
New Approach

scholarly journals Newly Developed Analytical Scheme and Its Applications to the Some Nonlinear Partial Differential Equations with the Conformable Derivative

2021 ◽  
Vol 5 (4) ◽  
pp. 238
Author(s):  
Li Yan ◽  
Gulnur Yel ◽  
Ajay Kumar ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rational Function ◽  
Analytical Approach ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Conformable Derivative ◽  
Partial Differential ◽  
Analytical Scheme

This paper presents a novel and general analytical approach: the rational sine-Gordon expansion method and its applications to the nonlinear Gardner and (3+1)-dimensional mKdV-ZK equations including a conformable operator. Some trigonometric, periodic, hyperbolic and rational function solutions are extracted. Physical meanings of these solutions are also presented. After choosing suitable values of the parameters in the results, some simulations are plotted. Strain conditions for valid solutions are also reported in detail.

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

scholarly journals Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Jacobi Elliptic Function ◽  
Deformation Method ◽  
Partial Differential ◽  
General Mapping

We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

scholarly journals Optical Solutions of Fokas-Lenells Equation via (m-1/G') - Expansion Method

2020 ◽  
Vol 7 ◽  
pp. 20-24
Author(s):  
Hasan Bulut ◽  
Khalid ◽  
Ban Jamal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Efficient Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Three Dimensions ◽  
Partial Differential ◽  
Wide Range

In this research paper, we investigate some novel soliton solutions to the perturbed Fokas-Lenells equation by using the (m + 1/G') expansion method. Some new solutions are obtained and they are plotted in two and three dimensions. This technique appears as a suitable, applicable, and efficient method to search for the exact solutions of nonlinear partial differential equations in a wide range. All gained optical soliton solutions are substituted into the FokasLenells equation and they verify it. The constraint conditions are also given.

scholarly journals A New Approach to Solve Nonlinear Partial Differential Equations

2007 ◽  
Vol 3 (4) ◽  
pp. 201-206 ◽  
Author(s):  
Abdoul R. Ghotbi ◽  
M. A. Mohammadza ◽  
A. Avaei ◽  
M. Keyvanipoo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
New Approach
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