scholarly journals Bilinear Equation and Additional Symmetries for an Extension of the Kadomtsev–Petviashvili Hierarchy

2021 ◽  
Vol 24 (3) ◽  
Author(s):  
Jiaping Lu ◽  
Chao-Zhong Wu
Keyword(s):  
Additional Symmetries ◽  
Bilinear Equation

A universal way to determine Hirota's bilinear equation of KdV type

2013 ◽  
Vol 54 (8) ◽  
pp. 081506
Author(s):  
Yi-Chao Ye ◽  
Zi-Xiang Zhou
Keyword(s):  
Bilinear Equation

The generalized additional symmetries of the two-Toda lattice hierarchy

2013 ◽  
Vol 54 (2) ◽  
pp. 023513 ◽  
Author(s):  
Jipeng Cheng ◽  
Ye Tian ◽  
Zhaowen Yan ◽  
Jingsong He
Keyword(s):  
Toda Lattice ◽  
Additional Symmetries ◽  
Toda Lattice Hierarchy

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

scholarly journals A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

2018 ◽  
Vol 07 (04) ◽  
pp. 1840001
Author(s):  
A. N. W. Hone ◽  
F. Zullo
Keyword(s):  
Taylor Series ◽  
Taylor Expansion ◽  
Tau Function ◽  
Tau Functions ◽  
Sigma Function ◽  
Special Cases ◽  
Hirota Bilinear Equation ◽  
Order Four ◽  
Hirota Bilinear ◽  
Bilinear Equation

We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the general form of the Taylor expansion around an arbitrary movable zero. The corresponding Taylor series for the tau-functions of the first and second Painlevé equations, as well as that for the Weierstrass sigma function, arise naturally as special cases, by setting certain parameters to zero.

scholarly journals Bianchi’s additional symmetries

2020 ◽  
Vol 15 (3-4) ◽  
pp. 455-462
Author(s):  
Alexander D. Rahm
Keyword(s):  
Additional Symmetries

scholarly journals Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

2009 ◽  
Vol 61 (6) ◽  
pp. 1201-1213 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
V. V. Dzhepko ◽  
Yu. G. Nikonorov
Keyword(s):  
Riemannian Manifold ◽  
Positive Integer ◽  
Lie Groups ◽  
Einstein Metrics ◽  
Homogeneous Spaces ◽  
Classical Groups ◽  
Stiefel Manifolds ◽  
Additional Symmetries

Abstract A Riemannian manifold (M, ρ) is called Einstein if the metric ρ satisfies the condition Ric(ρ) = c · ρ for some constant c. This paper is devoted to the investigation of G-invariant Einstein metrics, with additional symmetries, on some homogeneous spaces G/H of classical groups. As a consequence, we obtain new invariant Einstein metrics on some Stiefel manifolds SO(n)/SO(l). Furthermore, we show that for any positive integer p there exists a Stiefelmanifold SO(n)/SO(l) that admits at least p SO(n)-invariant Einstein metrics.

Additional symmetries for super KP hierarchies

1995 ◽  
Vol 87 (1-4) ◽  
pp. 105-108 ◽  
Author(s):  
Manuel Mañas ◽  
Luis Martínez Alonso ◽  
Elena Medina
Keyword(s):  
Additional Symmetries
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