Volterra Operator Algebra for Zero Curvature Representation. Universality of KP

1993 ◽  
pp. 126-131 ◽  
Author(s):  
A. Yu. Orlov
Keyword(s):  
Operator Algebra ◽  
Volterra Operator ◽  
Zero Curvature Representation ◽  
Zero Curvature

Generalized intermediate long‐wave hierarchy in zero‐curvature representation with noncommutative spectral parameter

1992 ◽  
Vol 33 (11) ◽  
pp. 3783-3793 ◽  
Author(s):  
A. Degasperis ◽  
D. Lebedev ◽  
M. Olshanetsky ◽  
S. Pakuliak ◽  
A. Perelomov ◽  
...  
Keyword(s):  
Spectral Parameter ◽  
Zero Curvature Representation ◽  
Zero Curvature ◽  
Long Wave

scholarly journals A Family of Integrable Differential-Difference Equations: Tri-Hamiltonian Structure and Lie Algebra of Vector Fields

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ning Zhang ◽  
Xi-Xiang Xu
Keyword(s):  
Spectral Problem ◽  
Lie Algebra ◽  
Difference Equations ◽  
Vector Fields ◽  
Hamiltonian Structure ◽  
Trace Identity ◽  
Zero Curvature Representation ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Liouville Integrable

Starting from a novel discrete spectral problem, a family of integrable differential-difference equations is derived through discrete zero curvature equation. And then, tri-Hamiltonian structure of the whole family is established by the discrete trace identity. It is shown that the obtained family is Liouville-integrable. Next, a nonisospectral integrable family associated with the discrete spectral problem is constructed through nonisospectral discrete zero curvature representation. Finally, Lie algebra of isospectral and nonisospectral vector fields is deduced.

ON SIGMA MODEL FORMULATION OF GREEN-SCHWARZ SUPERSTRING

1989 ◽  
Vol 04 (04) ◽  
pp. 351-359 ◽  
Author(s):  
A. ISAEV ◽  
E. IVANOV
Keyword(s):  
Direct Product ◽  
Sigma Model ◽  
Model Formulation ◽  
Field Equations ◽  
Zero Curvature Representation ◽  
Zero Curvature ◽  
Specific Choice ◽  
Target Manifold

The Green-Schwarz covariant superstring action is consistently deduced as the action of the Wess-Zumino-Witten σ-model defined on the direct product of two N = 1, D = 10 Poincaré supertranslation groups. N = 2 supersymmetry of the action is shown to be related to a specific choice of the target manifold. We propose a zero curvature representation for the GS superstring field equations and interpret the local fermionic supersymmetry of the GS action as a guage symmetry preserving this representation.

A 2-PARAMETER HIERARCHY OF INTEGRABLE LATTICE EQUATIONS

2008 ◽  
Vol 22 (14) ◽  
pp. 1389-1400
Author(s):  
XI-XIANG XU ◽  
WEI-LI CAO
Keyword(s):  
Toda Lattice ◽  
Special Choice ◽  
Hamiltonian Equation ◽  
Rational Form ◽  
Zero Curvature Representation ◽  
Zero Curvature ◽  
Integrable Lattice ◽  
Matrix Spectral Problem ◽  
Relativistic Toda Lattice ◽  
Liouville Integrable

A new discrete matrix spectral problem with two arbitrary constants is introduced, and the corresponding 2-parameter hierarchy of integrable lattice equations is obtained by discrete zero curvature representation. The resulting integrable lattice equations reduce to the hierarchy of relativistic Toda lattice in rational form for a special choice of the parameters. Moreover, a sub-hierarchy of the resulting integrable lattice equations is discussed. It is shown that each lattice equation in the sub-hierarchy is a Liouville integrable discrete Hamiltonian equation.

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