26 citations · 51 across the 14 of their papers we have counts for
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The Dunkl two-photon/Schrödinger algebras and their applications
Francisco J. Herranz, Danilo Latini
The work introduces the novel Dunkl two-photon and Dunkl-Schrödinger algebras as reflection-extended counterparts of the standard six-dimensional two-photon and Schrödinger algebra…
Generalized classical and quantum Zernike Hamiltonians
Francisco J. Herranz, Alfonso Blasco, Rutwig Campoamor-Stursberg +3
A superintegrable generalization of the classical and quantum Zernike systems is reviewed. The corresponding Hamiltonians are endowed with higher-order integrals and can be interpr…
Mixed superposition rules for Lie systems, compatible geometric structures, and applications
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz +1
Mixed superposition rules are, in short, a method to describe the general solutions of a time-dependent system of first-order differential equations, a so-called Lie system, in ter…
An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
Francisco J. Herranz, Danilo Latini
This work aims to bridge the gap between Dunkl superintegrable systems and the coalgebra symmetry approach to superintegrability, and subsequently to recover known models and const…
Nonlinear Lie-Hamilton systems: -Dependent curved oscillators and Kepler-Coulomb Hamiltonians
Rutwig Campoamor-Stursberg, Francisco J. Herranz, Javier de Lucas
The Lie-Hamilton approach for -dependent Hamiltonians is extended to cover the so-called nonlinear Lie-Hamilton systems, which are no longer related to a linear -dependent co…
Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz
We propose an adaptation of the notion of scaling symmetries for the case of Lie-Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of…
Generalized Buchdahl equations as Lie-Hamilton systems from the 'book' and oscillator algebras: Quantum deformations and their general solution
Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz
We revisit the nonlinear second-order differential equations where and are arbitrary functions on their argument f…
Lie-Hamilton systems on Riemannian and Lorentzian spaces from conformal transformations and some of their applications
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz
We propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spac…
A representation-theoretical approach to higher-dimensional Lie-Hamilton systems: The symplectic Lie algebra
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz
A new procedure for the construction of higher-dimensional Lie-Hamilton systems is proposed. This method is based on techniques belonging to the representation theory of Lie algebr…
Solutions by quadratures of complex Bernoulli differential equations and their quantum deformation
Rutwig Campoamor-Stursberg, Eduardo Fernandez-Saiz, Francisco J. Herranz
It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie-Hamilton system related to the book algebra can always…
Generalized time-dependent SIS Hamiltonian models: Exact solutions and quantum deformations
Eduardo Fernandez-Saiz, Rutwig Campoamor-Stursberg, Francisco J. Herranz
The theory of Lie-Hamilton systems is used to construct generalized time-dependent SIS epidemic Hamiltonians with a variable infection rate from the 'book' Lie algebra. Although th…
Jacobi-Lie systems: Fundamentals and low-dimensional classification
F. J. Herranz, J. de Lucas, C. Sardon
A Lie system is a system of differential equations describing the integral curves of a -dependent vector field taking values in a finite-dimensional real Lie algebra of vector f…
Lie-Hamilton systems on the plane: Applications and superposition rules
A. Blasco, F. J. Herranz, J. de Lucas +1
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a -dependent vector field taking values in a fin…