scholarly journals A non-Archimedean approach to prolongation theory

1986 ◽  
Vol 12 (3) ◽  
pp. 231-239 ◽  
Author(s):  
H. N. Van Eck
Keyword(s):  
Prolongation Theory

Complete Integrability Prolongation Structure and Backlund Transformation for the Konno-Onno Equation

2000 ◽  
Vol 55 (5) ◽  
pp. 545-549
Author(s):  
Chandan Kr. Das ◽  
A. Roy Chowdhury
Keyword(s):  
Positive Result ◽  
Explicit Form ◽  
Bäcklund Transformation ◽  
Lax Pair ◽  
Independent Study ◽  
Complete Integrability ◽  
Painlevé Test ◽  
Backlund Transformation ◽  
Prolongation Structure ◽  
Prolongation Theory

Abstract Painleve analysis is used to study the complete integrability of the recently proposed Konno-Onno equation, which also leads to a general form of solutions of the system. An independent study, using the prolongation theory, gives the explicit form of the Lax pair which is then used to obtain the Backlund transformation connecting two sets of solutions of the system. The existence of the Lax pair and the positive result of the Painleve test indicate the complete integrability of the system

Prolongation theory. A new nonlinear Schr�dinger equation

1987 ◽  
Vol 26 (7) ◽  
pp. 707-714 ◽  
Author(s):  
Swapna Roy ◽  
A. Roy Chowdhury
Keyword(s):  
Dinger Equation ◽  
Prolongation Theory

Prolongation Theory

1991 ◽  
pp. 236-265
Author(s):  
Robert L. Bryant ◽  
S. S. Chern ◽  
Robert B. Gardner ◽  
Hubert L. Goldschmidt ◽  
P. A. Griffiths
Keyword(s):  
Prolongation Theory

Prolongation theory of the three-wave resonant interaction

1985 ◽  
Vol 88 (2) ◽  
pp. 81-101 ◽  
Author(s):  
M. Leo ◽  
R. A. Leo ◽  
G. Soliani ◽  
L. Martina
Keyword(s):  
Resonant Interaction ◽  
Prolongation Theory

The Symmetry Group

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
New Approach ◽  
Prolongation Theory

This chapter, which ends Part II on some consequences of the new approach, introduces an alternative prolongation theory of Klein geometries that is more geometric and intuitive than the well-known prolongation theory of a linear Lie algebra developed by Guillemin, Singer, and Sternberg.

GEOMETRIC STRUCTURE OF THE HILBERT–YANG–MILLS FUNCTIONAL

2008 ◽  
Vol 05 (03) ◽  
pp. 387-405 ◽  
Author(s):  
A. PATÁK ◽  
D. KRUPKA
Keyword(s):  
Einstein Equations ◽  
Fiber Bundles ◽  
Variational Theory ◽  
Geometric Structures ◽  
Variation Formula ◽  
Yang Mills ◽  
Variational Functional ◽  
Fibered Manifolds ◽  
Prolongation Theory ◽  
Principal Fiber Bundles

The global variational functional, defined by the Hilbert–Yang–Mills Lagrangian over a smooth manifold, is investigated within the framework of prolongation theory of principal fiber bundles, and global variational theory on fibered manifolds. The principal Lepage equivalent of this Lagrangian is constructed, and the corresponding infinitesimal first variation formula is obtained. It is shown, in particular, that the Noether currents, associated with isomorphisms of the underlying geometric structures, split naturally into several terms, one of which is the exterior derivative of the Komar–Yang–Mills superpotential. Consequences of invariance of the Hilbert–Yang–Mills Lagrangian under isomorphisms of underlying geometric structures such as Noether's conservation laws for global currents are then established. As an example, a general formula for the Komar–Yang–Mills superpotential of the Reissner–Nordström solution of the Einstein equations is found.

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