scholarly journals Exact solutions of some nonlinear systems of partial differential equations by using the first integral method

2012 ◽  
Vol 387 (2) ◽  
pp. 807-814 ◽  
Author(s):  
K. Hosseini ◽  
R. Ansari ◽  
P. Gholamin
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
First Integral ◽  
Partial Differential ◽  
First Integral Method

scholarly journals New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shoukry Ibrahim Atia El-Ganaini
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integrals ◽  
Partial Differential ◽  
First Integral Method ◽  
New Exact Solutions

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

First integral method for non-linear differential equations with conformable derivative

2018 ◽  
Vol 13 (1) ◽  
pp. 14 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar ◽  
Abdon Atangana
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
General Scheme ◽  
First Integral ◽  
Fractional Partial Differential Equations ◽  
Conformable Derivative ◽  
First Integral Method ◽  
Analytic Treatment ◽  
Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

Exact solutions for the fractional differential equations by using the first integral method

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Hossein Aminikhah ◽  
A. Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Commutative Algebra ◽  
Integral Method ◽  
First Integral ◽  
Ring Theory ◽  
First Integral Method ◽  
Fractional Differential ◽  
Method Show

AbstractIn this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-Kaup-Like systems. This method is based on the ring theory of commutative algebra. The results obtained by the proposed method show that the approach is effective and general. This approach can also be applied to other nonlinear fractional differential equations, which are arising in the theory of solitons and other areas.

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