scholarly journals POLYNOMIAL FIRST INTEGRALS FOR THE CHEN AND LÜ SYSTEMS

2012 ◽  
Vol 22 (11) ◽  
pp. 1250262 ◽  
Author(s):  
JAUME LLIBRE ◽  
CLAUDIA VALLS
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Method Of Characteristics ◽  
First Integrals ◽  
Homogeneous Polynomials ◽  
Partial Differential ◽  
The Method Of Characteristics

We characterize all the values of the parameters for which the Chen and Lü systems have polynomial first integrals by using weight homogeneous polynomials and the method of characteristics for solving partial differential equations. We improve previous results which were not complete.

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.

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