An improved coarse-mesh nodal integral method for partial differential equations

1997 ◽  
Vol 13 (2) ◽  
pp. 113-145 ◽  
Author(s):  
Rizwan-uddin
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Method ◽  
Coarse Mesh ◽  
Partial Differential ◽  
Nodal 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.

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