Two types of new Lie algebras and corresponding hierarchies of evolution equations

2003 ◽  
Vol 310 (1) ◽  
pp. 19-24 ◽  
Author(s):  
Yufeng Zhang
Keyword(s):  
Lie Algebras ◽  
Evolution Equations

scholarly journals The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras

1981 ◽  
Vol 1 (3) ◽  
pp. 361-380 ◽  
Author(s):  
George Wilson
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Toda Lattice ◽  
Evolution Equations ◽  
Gordon Equation ◽  
Two Dimensional ◽  
Simple Lie Algebras ◽  
Kdv Equations ◽  
Modified Kdv Equations ◽  
Toda Lattice Equations

AbstractWe associate to each complex simple Lie algebra g a hierarchy of evolution equations; in the simplest case g = sl(2) they are the modified KdV equations. These new equations are related to the two-dimensional Toda lattice equations associated with g in the same way that the modified KdV equations are related to the sinh-Gordon equation.

A NEW SOLITON HIERARCHY AND ITS TWO KINDS OF EXPANDING INTEGRABLE MODELS AS WELL AS HAMILTONIAN STRUCTURE

2009 ◽  
Vol 23 (14) ◽  
pp. 3059-3072
Author(s):  
YUFENG ZHANG ◽  
HUANHE DONG ◽  
Y. C. HON
Keyword(s):  
Quadratic Form ◽  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Integrable Models ◽  
Loop Algebras ◽  
Soliton Hierarchy

With the help of two different Lie algebras and the corresponding loop algebras, the first and second kind of expanding integrable models of a new soliton hierarchy of evolution equations are obtained, respectively. The Hamiltonian structure of the first one is worked out by the quadratic-form identity. The bi-Hamiltonian structure of the second one is also generated. From the paper, we conclude that various Lie algebras really produce different soliton hierarchies of evolution equations. The approach presented in the paper provides a way for generating different integrable soliton expanding systems of the known soliton hierarchy of equations.

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