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pro vyhledávání: '"Fordy, Allan P"'
Autor:
Fordy, Allan P
In this paper we discuss the Painlev\'e reductions of coupled KdV systems. We start by comparing the procedure with that of {\em stationary reductions}. Indeed, we see that exactly the same construction can be used at each step and parallel results o
Externí odkaz:
http://arxiv.org/abs/2405.09694
Autor:
Fordy, Allan P., Huang, Qing
In this paper we continue our analysis of the stationary flows of $M$ component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the $t_1$ and $t_2$ flows, using the case $M=3$ as our main example. One of
Externí odkaz:
http://arxiv.org/abs/2307.03294
Autor:
Fordy, Allan P., Huang, Qing
Publikováno v:
SIGMA 19 (2023), 015, 34 pages
In this paper we revisit the subject of stationary flows of Lax hierarchies of a coupled KdV class. We explain the main ideas in the standard KdV case and then consider the dispersive water waves (DWW) case, with respectively 2 and 3 Hamiltonian repr
Externí odkaz:
http://arxiv.org/abs/2210.12771
Autor:
Fordy, Allan P., Huang, Qing
We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system as a particular case. For the general class, we introduce separation coordinates to
Externí odkaz:
http://arxiv.org/abs/2111.15659
Autor:
Fordy, Allan P., Huang, Qing
Publikováno v:
In Journal of Geometry and Physics March 2024 197
Autor:
Fordy, Allan P., Huang, Qing
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the problem o
Externí odkaz:
http://arxiv.org/abs/2009.11653
Autor:
Fordy, Allan P.
We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall-Sheffer operators, with polynomi
Externí odkaz:
http://arxiv.org/abs/2001.10593
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Autor:
Fordy, Allan P., Huang, Qing
We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional {\em quadratic} first integrals, thus constructing a large class of
Externí odkaz:
http://arxiv.org/abs/1910.08836
Autor:
Fordy, Allan P., Galajinsky, Anton
The Eisenhart lift is a variant of geometrization of classical mechanics with $d$ degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on $(d+2)$-dimensional spacetime of Lore
Externí odkaz:
http://arxiv.org/abs/1901.03699