Publications (16)
General Nth order integrals of the motion
S. Post, P. Winternitz
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and…
A family of fourth-order superintegable systems with rational potentials related to Painlevé VI
I. Marquette, S. Post, L. Ritter
We discuss a family of Hamiltonians given by particular rational extensions of the singular oscillator in two-dimensions. The wave functions of these Hamiltonians can be expressed…
Laplace-type equations as conformal superintegrable systems
E. G. Kalnins, J. M. Kress, W. Miller +1
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(…
Analysis of sigma models via projective structure
S. Post, A. M. Grundland
In this paper, we study rank-1 projector solutions to the completely integrable Euclidean sigma model in two dimension and their associated surfaces immersed in the $su(…
Third-order superintegrable systems with potentials satisfying nonlinear equations
A. Marchesiello, S. Post, L. Å nobl
The conditions for superintegrable systems in two-dimensional Euclidean space admitting separation of variables in an orthogonal coordinate system and a functionally independent th…
Third-order superintegrable systems separable in parabolic coordinates
I. Popper, S. Post, P. Winternitz
In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equa…
Soliton surfaces associated with sigma models; differential and algebraic aspect
P. P. Goldstein, A. M. Grundland, S. Post
In this paper, we consider both differential and algebraic properties of surfaces associated with sigma models. It is shown that surfaces defined by the generalized Weierstrass for…
Soliton surfaces associated with CP^{N-1} sigma models
A. M. Grundland, S. Post
Soliton surfaces associated with CP^{N-1} sigma models are constructed using the Generalized Weierstrass and the Fokas-Gel'fand formulas for immersion of 2D surfaces in Lie algebra…
Soliton surfaces associated with symmetries of ODEs written in Lax representation
A. M. Grundland, S. Post
The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally de…
Soliton surfaces associated with generalize symmetries of integrable equations
A. M. Grundland, S. Post
In this paper, based on the Fokas, Gel'fand et al approach [15,16], we provide a symmetry characterization of continuous deformations of soliton surfaces immersed in a Lie algebra…
Coupling constant metamorphosis and Nth order symmetries in classical and quantum mechanics
E. G. Kalnins, W. Miller, S. Post
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into othe…
Supersymmetric Quantum Mechanics with Reflections
S. Post, L. Vinet, A. Zhedanov
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Sc…
Surfaces immersed in Lie algebras associated with elliptic integrals
A. M. Grundland, S. Post
The main aim of this paper is to study soliton surfaces immersed in Lie algebras associated with ordinary differential equations (ODE's) for elliptic functions. That is, given a li…
An infinite family of superintegrable deformations of the Coulomb potential
S. Post, P. Winternitz
We introduce a new family of Hamiltonians with a deformed Kepler- Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all ration…
Soliton surfaces and generalized symmetries of integrable systems
A. M. Grundland, S. Post, D. Riglioni
In this paper, we discuss some specific features of symmetries of integrable systems which can be used to contruct the Fokas-Gel'fand formula for the immersion of 2D-soliton surfac…
Soliton surfaces via zero-curvature representation of differential equations
A. M. Grundland, S. Post
The main aim of this paper is to introduce a new version of the Fokas-Gel'fand formula for immersion of soliton surfaces in Lie algebras. The paper contains a detailed exposition o…