Modified Auxiliary Differential Equation Method and Exact Solutions Generalized Schrödinger

2014 ◽  
Vol 513-517 ◽  
pp. 4470-4473 ◽  
Author(s):  
Lin Tian ◽  
Yu Ping Qin
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Hyperbolic Function ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Solution ◽  
Auxiliary Differential Equation Method ◽  
Differential Equation Method

This paper describes a method on which modify auxiliary differential equation method by using this method for solving nonlinear partial differential equations and with aid of Maple Software ,we get the exact solution of the generalized schrödinger, including hyperbolic function solutions, trigonometric solution.

The Multiple Exact Solutions for the Variable Coefficient KdV Equation

2014 ◽  
Vol 513-517 ◽  
pp. 4474-4477
Author(s):  
Lin Tian ◽  
Jia Qing Miao
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Auxiliary Differential Equation Method ◽  
Differential Equation Method

The auxiliary differential equation method has recently been proposed ,It is introduced to construct more new exact solutions for the variable coefficient KdV equations. As a result , hyperbolic function solutions, trigonometric function solutions, and elliptic function solutions rational function solutions with parameters are obtained.

scholarly journals Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 129-139 ◽  
Author(s):  
EL Sayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Power Law ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Pdes ◽  
Hyperbolic Function ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Hyperbolic Function Solutions ◽  
Fibonacci Function

AbstractIn this article, we apply the generalized Kudryashov method for finding exact solutions of three nonlinear partial differential equations (PDEs), namely: the Biswas-Milovic equation with dual-power law nonlinearity; the Zakharov--Kuznetsov equation (ZK(m,n,k)); and the K(m,n) equation with the generalized evolution term. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, and hyperbolic function solutions. Physical explanations for certain solutions of the three nonlinear PDEs are obtained.

scholarly journals FDTD Modeling of Lorentzian DNG Metamaterials by Auxiliary Differential Equation Method

2014 ◽  
Vol 06 (05) ◽  
pp. 106-114 ◽  
Author(s):  
Chiranjib Goswami ◽  
Saptarshi Mukherjee ◽  
Subrata Karmakar ◽  
Manimala Pal ◽  
Rowdra Ghatak
Keyword(s):  
Differential Equation ◽  
Equation Method ◽  
Auxiliary Differential Equation Method ◽  
Differential Equation Method
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