A generalized auxiliary equation method and its application to nonlinear Klein–Gordon and generalized nonlinear Camassa–Holm equations

2008 ◽  
Vol 372 (7) ◽  
pp. 1048-1060 ◽  
Author(s):  
Emmanuel Yomba
Keyword(s):  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Klein Gordon ◽  
Generalized Auxiliary Equation Method

A Generalized Auxiliary Equation Method for the Quadratic Nonlinear KG Equation

2013 ◽  
Vol 394 ◽  
pp. 571-576
Author(s):  
Sheng Zhang ◽  
Bo Xu ◽  
Ao Xue Peng
Keyword(s):  
Partial Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Mathematical Tool ◽  
Auxiliary Equation Method ◽  
Klein Gordon ◽  
Generalized Auxiliary Equation Method ◽  
Powerful Mathematical Tool

A generalized auxiliary equation method with symbolic computation is used to construct more general exact solutions of the quadratic nonlinear Klein-Gordon (KG) equation. As a result, new and more general solutions are obtained. It is shown that the generalized auxiliary equation method provides a more powerful mathematical tool for solving nonlinear partial differential equations arising in the fields of nonlinear sciences.

Auxiliary Equation Method for Fractional Differential Equations with Modified Riemann–Liouville Derivative

2016 ◽  
Vol 17 (7-8) ◽  
pp. 413-420 ◽  
Author(s):  
Arzu Akbulut ◽  
Melike Kaplan ◽  
Ahmet Bekir
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
Liouville Derivative ◽  
Regularized Long Wave Equation ◽  
Klein Gordon ◽  
Fractional Differential

Abstract:In this work, the auxiliary equation method is applied to derive exact solutions of nonlinear fractional Klein–Gordon equation and space-time fractional Symmetric Regularized Long Wave equation. Consequently, some exact solutions of these equations are successfully obtained. These solutions are formed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie’s modified Riemann–Liouville sense. The exact solutions founded by the suggested method indicate that the approach is easy to implement and powerful.

scholarly journals Exact Travelling Wave Solutions for Space-Time Fractional Klein-Gordon Equation and (2+1)-Dimensional Time-Fractional Zoomeron Equation via Auxiliary Equation Method

2020 ◽  
Vol 5 (1) ◽  
pp. 437-446 ◽  
Author(s):  
Muammer Topsakal ◽  
Filiz TaŞcan
Keyword(s):  
Gordon Equation ◽  
Travelling Wave ◽  
Space Time ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method ◽  
New Exact Solutions ◽  
Different Types ◽  
Klein Gordon ◽  
Klein Gordon Equation

AbstractIn this paper, the new exact solutions of nonlinear conformable fractional partial differential equations(CFPDEs) are achieved by using auxiliary equation method for the nonlinear space-time fractional Klein-Gordon equation and the (2+1)-dimensional time-fractional Zoomeron equation. The technique is easily applicable which can be applied successfully to get the solutions for different types of nonlinear CFPDEs. The conformable fractional derivative(CFD) definitions are used to cope with the fractional derivatives.

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