scholarly journals Quantum Cohomology and the Periodic Toda Lattice

2001 ◽  
Vol 217 (3) ◽  
pp. 475-487 ◽  
Author(s):  
Martin A. Guest ◽  
T. Otofuji
Keyword(s):  
Toda Lattice ◽  
Quantum Cohomology

scholarly journals An affine quantum cohomology ring for flag manifolds and the periodic Toda lattice

2017 ◽  
Vol 116 (1) ◽  
pp. 135-181
Author(s):  
Augustin-Liviu Mare ◽  
Leonardo C. Mihalcea
Keyword(s):  
Toda Lattice ◽  
Cohomology Ring ◽  
Quantum Cohomology ◽  
Flag Manifolds

Change of the Time for the Toda Lattice

2001 ◽  
Vol 8 (Supplement) ◽  
pp. 278
Author(s):  
A V TSIGANOV
Keyword(s):  
Toda Lattice

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

Casoratian Solutions to Toda Lattice Via Its Bäcklund Transformation

2010 ◽  
Vol 53 (3) ◽  
pp. 435-439
Author(s):  
Xuan Qi-Fei ◽  
Zhang Da-Jun ◽  
Zhou Jing
Keyword(s):  
Toda Lattice ◽  
Bäcklund Transformation ◽  
Backlund Transformation

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.

Periodic solutions of Toda lattice in loop nonlinear transmission line

1993 ◽  
Vol 29 (7) ◽  
pp. 607 ◽  
Author(s):  
G.J. Ballantyne ◽  
P.T. Gough ◽  
D.P. Taylor
Keyword(s):  
Transmission Line ◽  
Periodic Solutions ◽  
Toda Lattice ◽  
Nonlinear Transmission Line ◽  
Nonlinear Transmission
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