scholarly journals The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups

1981 ◽  
Vol 65 (3) ◽  
pp. 861-876 ◽  
Author(s):  
B. Fuchssteiner
Keyword(s):  
Lie Algebra ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Symmetry Groups ◽  
Algebra Structure ◽  
Infinite Dimensional

APPLICATIONS OF THE LIE ALGEBRA gl(2)

2009 ◽  
Vol 23 (14) ◽  
pp. 1763-1770 ◽  
Author(s):  
YUFENG ZHANG ◽  
HONWAH TAM
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Lie Algebra ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Nonlinear Evolution Equations ◽  
Backlund Transformation

With the help of a subalgebra of the Lie algebra gl (2) (still denoted by gl (2)), a non-isospectral evolution-equation hierarchy is obtained, whose reduction is similar to that given by Li. Employing the Lie algebra gl (2) again, we work out nonlinear evolution equations with exponential terms and produce their Bäcklund Transformation as well as some exact solutions.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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