scholarly journals Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety

2006 ◽  
pp. 175-203
Author(s):  
Kanehisa Takasaki
Keyword(s):  
Spectral Parameter ◽  
Grassmann Variety ◽  
Infinite Dimensional

DEFORMATIONS OF LOOP ALGEBRAS AND CLASSICAL INTEGRABLE SYSTEMS: FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

2004 ◽  
Vol 16 (07) ◽  
pp. 823-849 ◽  
Author(s):  
T. SKRYPNYK
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Systems ◽  
Spectral Parameter ◽  
Integrable Systems ◽  
Integrable Hamiltonian Systems ◽  
Infinite Dimensional ◽  
Loop Algebras ◽  
Finite Dimensional ◽  
Quasigraded Lie Algebras ◽  
Classical Integrable

We construct a family of infinite-dimensional quasigraded Lie algebras, that could be viewed as deformation of the graded loop algebras and admit Kostant–Adler scheme. Using them we obtain new integrable hamiltonian systems admitting Lax-type representations with the spectral parameter.

scholarly journals Integrability structures of the generalized Hunter–Saxton equation

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Oleg I. Morozov
Keyword(s):  
Lie Algebra ◽  
Spectral Parameter ◽  
Infinite Number ◽  
Higher Order ◽  
Lax Representation ◽  
Recursion Operators ◽  
Higher Symmetries ◽  
Infinite Dimensional ◽  
Infinite Dimensional Lie Algebra

AbstractWe consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give examples of employing the higher order symmetries to constructing exact globally defined solutions for the generalized Hunter–Saxton equation.

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