scholarly journals Higher-Order Kinematics in Dual Lie Algebra

2020 ◽  
Author(s):  
Daniel Condurache
Keyword(s):  
Lie Algebra ◽  
Higher Order

scholarly journals Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Oguzhan Kasikci ◽  
Nese Ozdemir ◽  
Mehmet Ozkan ◽  
Utku Zorba
Keyword(s):  
Lie Algebra ◽  
Three Dimensional ◽  
Higher Order

Infinitesimal Kinematics Methods in the Mobility Determination of Kinematic Chains

2009 ◽  
Author(s):  
J. M. Rico ◽  
J. J. Cervantes ◽  
A. Tadeo ◽  
J. Gallardo ◽  
L. D. Aguilera ◽  
...  
Keyword(s):  
Lie Algebra ◽  
Good Deal ◽  
Higher Order ◽  
The Other ◽  
Velocity Analysis ◽  
Euclidean Group ◽  
Kinematic Chains ◽  
Order Analysis ◽  
The One

In recent years, there has been a good deal of controversy about the application of infinitesimal kinematics to the mobility determination of kinematic chains. On the one hand, there has been several publications that promote the use of the velocity analysis, without any additional results, for the determination of the mobility of kinematic chains. On the other hand, the authors of this contribution have received several reviews of researchers who have the strong belief that no infinitesimal method can be used to correctly determine the mobility of kinematic chains. In this contributions, it is attempted to show that velocity analysis by itself can not correctly determine the mobility of kinematic chains. However, velocity and higher order analysis coupled with some recent results about the Lie algebra, se(3), of the Euclidean group, SE(3), can correctly determine the mobility of kinematic chains.

scholarly journals Multilocal invariants for the classical groups

2003 ◽  
Vol 2003 (1) ◽  
pp. 27-63
Author(s):  
Paul F. Dhooghe
Keyword(s):  
Lie Algebra ◽  
Higher Order ◽  
Transformation Groups ◽  
Representation Space ◽  
Classical Groups ◽  
Invariant Polynomials ◽  
Lie Transformation ◽  
Capelli Identities

Multilocal higher-order invariants, which are higher-order invariants defined at distinct points of representation space, for the classical groups are derived in a systematic way. The basic invariants for the classical groups are the well-known polynomial or rational invariants as derived from the Capelli identities. Higher-order invariants are then constructed from the former ones by means of total derivatives. At each order, it appears that the invariants obtained in this way do not generate all invariants. The necessary additional invariants are constructed from the invariant polynomials on the Lie algebra of the Lie transformation groups.

The prolongation structure of a higher order Korteweg-de Vries equation

1978 ◽  
Vol 358 (1694) ◽  
pp. 287-296 ◽  
Keyword(s):  
Lie Algebra ◽  
Vries Equation ◽  
Higher Order ◽  
De Vries ◽  
Prolongation Structure

We have used Wahlquist & Estabrook’s prolongation method to construct a Lie algebra for the higher order Korteweg de Vries (K.deV.) equation q 4 x + α qq 2 x + β q 2 x + γ q 3 ) x + q t = 0 with ( q nx =

scholarly journals WKB periods for higher order ODE and TBA equations

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Katsushi Ito ◽  
Takayasu Kondo ◽  
Kohei Kuroda ◽  
Hongfei Shu
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Field Equation ◽  
Lie Algebra ◽  
Bethe Ansatz ◽  
Linear Problem ◽  
Higher Order ◽  
Quantum Corrections ◽  
Order Ordinary Differential Equation ◽  
Quadratic Potential

Abstract We study the WKB periods for the (r + 1)-th order ordinary differential equation (ODE) which is obtained by the conformal limit of the linear problem associated with the $$ {A}_r^{(1)} $$ A r 1 affine Toda field equation. We compute the quantum corrections by using the Picard-Fuchs operators. The ODE/IM correspondence provides a relation between the Wronskians of the solutions and the Y-functions which satisfy the thermodynamic Bethe ansatz (TBA) equation related to the Lie algebra Ar. For the quadratic potential, we propose a formula to show the equivalence between the logarithm of the Y-function and the WKB period, which is confirmed by solving the TBA equation numerically.

scholarly journals Integrability structures of the generalized Hunter–Saxton equation

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Oleg I. Morozov
Keyword(s):  
Lie Algebra ◽  
Spectral Parameter ◽  
Infinite Number ◽  
Higher Order ◽  
Lax Representation ◽  
Recursion Operators ◽  
Higher Symmetries ◽  
Infinite Dimensional ◽  
Infinite Dimensional Lie Algebra

AbstractWe consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give examples of employing the higher order symmetries to constructing exact globally defined solutions for the generalized Hunter–Saxton equation.

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