Symplectic structure, Lagrangian, and involutiveness of first integrals of the principal chiral field equation

1983 ◽  
Vol 87 (4) ◽  
pp. 505-513 ◽  
Author(s):  
L. A. Dickey
Keyword(s):  
Field Equation ◽  
Symplectic Structure ◽  
First Integrals ◽  
Chiral Field ◽  
Principal Chiral Field

scholarly journals Fractional derivative of inverse matrix and its applications to soliton theory

2020 ◽  
Vol 24 (4) ◽  
pp. 2597-2604
Author(s):  
Sheng Zhang ◽  
Jiao Gao ◽  
Bo Xu
Keyword(s):  
Field Equation ◽  
Fractional Derivative ◽  
Partial Derivative ◽  
Inverse Matrix ◽  
Chiral Field ◽  
Soliton Theory ◽  
Yang Mills ◽  
Principal Chiral Field ◽  
Linear Pde ◽  
Non Linear

In this paper, a formula of the local fractional partial derivative of inverse matrix is presented and proved. With the help of the derived formula, two new non-linear PDE are derived including the local fractional non-isospectral self-dual Yang-Mills equation and the local fractional principal chiral field equation. It is shown that the formula of the local fractional partial derivative of inverse matrix can be used to derive some other local fractional non-linear PDE in soliton theory.

Integrability of the principal chiral field model in 1 + 1 dimension

1986 ◽  
Vol 167 (2) ◽  
pp. 227-256 ◽  
Author(s):  
L.D Faddeev ◽  
N.Yu Reshetikhin
Keyword(s):  
Field Model ◽  
Chiral Field ◽  
Principal Chiral Field
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