The Connection between the Riemann-Hilbert transformation and the Poisson bracket for Lax pair systems

Ge, Mo-Lin; Xue, Kang

doi:10.1016/S0375-9601(97)00904-3

The Connection between the Riemann-Hilbert transformation and the Poisson bracket for Lax pair systems

Mo-Lin Ge
(
- Changchun, Northeast Normal U.
)
,
Kang Xue
(
- Changchun, Northeast Normal U. and
- Jilin U.
)

Feb, 1998

5 pages

Published in:

Phys.Lett.A 238 (1998) 344-348

DOI:

10.1016/S0375-9601(97)00904-3

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Abstract: (Elsevier)

The Riemann-Hilbert transformation (RHT) for Lax-pair systems is shown to be connected with the Poisson bracket description. We set up the classically canonical formulation for the variation of Φ ( x , t ; λ ) in terms of the Poisson bracket between the corresponding conserved quantities and Φ ( x , t ; λ ), where Φ ( x , t ; λ ) satisfies the Lax-pair condition and the variation preserves the equation of motion.

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The Connection between the Riemann-Hilbert transformation and the Poisson bracket for Lax pair systems

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The Group Theoretical Aspects of Infinitesimal Riemann-hilbert Transform and Hidden Symmetry

RIEMANN-HILBERT TRANSFORMS AND BIANCHI-BACKLUND TRANSFORMATIONS FOR THE SUPERSYMMETRIC YANG-MILLS FIELDS

KAC-MOODY ALGEBRA FROM INFINITESIMAL RIEMANN-HILBERT TRANSFORM

Kac-Moody Algebra Is Hidden Symmetry of Chiral Models

A Generating Function for Hidden Symmetries of Chiral Models

An Explicit Approach to the Group Structure of Hidden Symmetry

An Introduction to Yangian Symmetries

Quantization of the selfdual Yang-Mills system: Algebras and hierarchy

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