Multi-Hamiltonian structure of kdv hierarchy by Drienfeld-Sokolov formalism

1996 ◽  
Vol 35 (5) ◽  
pp. 903-909
Author(s):  
Swapna Ray Jain
Keyword(s):  
Hamiltonian Structure ◽  
Kdv Hierarchy

scholarly journals REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KdV HIERARCHIES AND THE TWO-MATRIX MODEL

1995 ◽  
Vol 10 (17) ◽  
pp. 2537-2577 ◽  
Author(s):  
H. ARATYN ◽  
E. NISSIMOV ◽  
S. PACHEVA ◽  
A.H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Hamiltonian Structure ◽  
Toda Lattice ◽  
Free Field ◽  
String Model ◽  
Matrix Formulation ◽  
Hamiltonian Action ◽  
Kdv Hierarchy ◽  
Associated Matrix ◽  
Toda Lattice Hierarchy

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL (M+1, M−k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL (M+1, M−k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M−k) Poisson bracket algebras generalizing the familiar nonlinear WM+1 algebra. Discrete Bäcklund transformations for SL (M+1, M−k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL (M+1, 1) KdV hierarchy.

scholarly journals ON GAUGE-EQUIVALENT FORMULATIONS OF N=4 SKdV HIERARCHY

1998 ◽  
Vol 13 (35) ◽  
pp. 2855-2862 ◽  
Author(s):  
E. IVANOV
Keyword(s):  
Hamiltonian Structure ◽  
Superconformal Algebra ◽  
Kdv Hierarchy ◽  
Small N

We point out that the N=4 supersymmetric KdV hierarchy, when written through the prepotentials of the bosonic chiral and antichiral N=2 supercurrents, exhibits a freedom related to the possibility to choose different gauges for the prepotentials. Some implications of this property are presented. In particular, we give the prepotential form of the "small" N=4 superconformal algebra, the second Hamiltonian structure algebra of the N=4 SKdV hierarchy, for two choices of gauge.

A FRACTIONAL KdV HIERARCHY

1991 ◽  
Vol 06 (17) ◽  
pp. 1561-1573 ◽  
Author(s):  
IOANNIS BAKAS ◽  
DIDIER A. DEPIREUX
Keyword(s):  
Hamiltonian Structure ◽  
Boussinesq Equation ◽  
Operator Algebras ◽  
Nonlinear Differential Equations ◽  
Conserved Quantities ◽  
Gauge Groups ◽  
Yang Mills ◽  
Kdv Hierarchy ◽  
Alternative Set ◽  
New System

We construct a new system of integrable nonlinear differential equations associated with. the operator algebra [Formula: see text] of Polyakov. Its members are fractional generalizations of KdV type flows corresponding to an alternative set of constraints on the 2-dim. SL(3) gauge connections. We obtain the first non-trivial examples by dimensional reductiion from self-dual Yang–Mills and then generate recursively the entire hierarchy and its conserved quantities using a bi-Hamiltonian structure. Certain relations with the Boussinesq equation are also discussed together with possible generalizations of the formalism to SL (N) gauge groups and [Formula: see text] operator algebras with arbitrary N and l.

scholarly journals Hamiltonian Structure and Coset Construction of the Supersymmetric Extensions of N=2 KdV Hierarchy

1997 ◽  
Vol 12 (39) ◽  
pp. 3037-3049
Author(s):  
L. Bonora ◽  
S. Krivonos
Keyword(s):  
Hamiltonian Structure ◽  
Kdv Hierarchy ◽  
Coset Construction

A manifestly N=2 supersymmetric coset formalism is applied to analyze the "fermionic" extensions of N=2, a=4 and a=-2 KdV hierarchies. Both hierarchies can be obtained from a manifest N=2 coset construction. This coset is defined as the quotient of some local but nonlinear superalgebra by a Û (1) subalgebra. Three superextensions of N=2 KdV hierarchy are proposed, among which one seems to be entirely new.

scholarly journals Two Kinds of New Integrable Couplings of the Negative-Order Korteweg-de Vries Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Binlu Feng ◽  
Yufeng Zhang
Keyword(s):  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Vries Equation ◽  
Kdv Hierarchy ◽  
Kdv Equations ◽  
Loop Algebras ◽  
Negative Order ◽  
Integrable Couplings ◽  
De Vries ◽  
Integrable Coupling

Based on some known loop algebras with finite dimensions, two different negative-order integrable couplings of the negative-order Korteweg-de Vries (KdV) hierarchy of evolution equations are generated by making use of the Tu scheme, from which the corresponding negative-order integrable couplings of the negative-order KdV equations are followed to be obtained. The resulting Hamiltonian structure of one negative integrable coupling is derived from the variational identity.

THE N = 3 SUPERSYMMETRIC KdV HIERARCHY

1993 ◽  
Vol 08 (12) ◽  
pp. 1161-1169 ◽  
Author(s):  
C. M. YUNG
Keyword(s):  
Conservation Law ◽  
Hamiltonian Structure ◽  
Kdv Equation ◽  
Superconformal Algebra ◽  
Supersymmetric Extension ◽  
Kdv Hierarchy ◽  
The Kdv Equation

An N = 3 supersymmetric extension of the KdV equation, whose Hamiltonian structure is the classical O(3)-extended superconformal algebra is presented. Integrability of the equation is argued based on the existence of a non-trivial conservation law which reduces to the first non-trivial conservation law of the KdV equation.

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