Recent Developments in Integrable Systems and Related Topics of Mathematical Physics

By a curious chronological coincidence, the tercentenary of Newton’s birth in 1642 is succeeded by the centenary of another outstanding event in the history of mathematics; the discovery of Quaternions in 1843 by Sir W. R. Hamilton. It seems a suitable occasion for drawing attention to the extent to which conceptions due to Irish mathematicians of that epoch are interwoven into the technique employed in recent developments in mathematical physics.

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Editors’ preface for the topical issue “Finite dimensional integrable systems, dynamics, and Lie theoretic methods in Geometry and Mathematical Physics”

Central European Journal of Mathematics ◽

10.2478/s11533-012-0092-9 ◽

2012 ◽

Vol 10 (5) ◽

pp. 1593-1595

Author(s):

Andreas Čap ◽

Vladimir S. Matveev ◽

Karin Melnick ◽

Galliano Valent

Keyword(s):

Integrable Systems ◽

Mathematical Physics ◽

Systems Dynamics ◽

Topical Issue ◽

Finite Dimensional

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Topology, Geometry, Integrable Systems, and Mathematical Physics

10.1090/trans2/234 ◽

2014 ◽

Cited By ~ 2

Keyword(s):

Integrable Systems ◽

Mathematical Physics

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Special Issue on Recent Developments in Infinite Dimensional Algebras and their Applications to Quantum Integrable Systems

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/40/30/e01 ◽

2007 ◽

Vol 40 (30) ◽

Author(s):

Andreas Fring, Petr Kulish, Nenad M Samtleben

Keyword(s):

Integrable Systems ◽

Quantum Integrable Systems ◽

Special Issue ◽

Infinite Dimensional ◽

Recent Developments

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Integrable systems connected with black holes

Communications of the Byurakan Astrophysical Observatory ◽

10.52526/25792776-2019.66.1-89 ◽

2019 ◽

pp. 89-93

Author(s):

H. Demirchian

Keyword(s):

Black Holes ◽

Shock Waves ◽

Gravitational Waves ◽

Integrable Systems ◽

Mathematical Physics ◽

Theory Of Relativity ◽

Test Particles ◽

Special Cases ◽

A New Technique ◽

Definition Of

We studied some important questions in general relativity and mathematical physics mainly related to the two most important solutions of the theory of relativity - gravitational waves and black holes. In particular, the work is related to astrophysical shock waves, gravitational waves, black holes, integrable systems associated with them as well as their quantum equivalents. We studied the effects of null shells on geodesic congruences and suggested a general covariant definition of the gravitational memory effect. Thus, we studied observable effects that astrophysical shock waves can have on test particles after cataclysmic astrophysical events. We studied the geodesics of massive particles in Near Horizon Extremal Myers-Perry (NHEMP) black hole geometries. This is the space-time in the vicinity of the horizon of higher dimensional rotating black holes. Thus, this work can have applications for studying accretions of black holes. The system is also important in mathematical physics as it describes integrable (in special cases superintegrable) system, where the constants of motion are fully studied. On the other hand, the quantum counterparts of this and other integrable systems are studied as well and a new technique is suggested for geometrization of these systems.

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