91 citations · 1.2k across the 114 of their papers we have counts for
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On Haantjes tensors for second-order superintegrable systems
Ian Marquette, Damien McLeod, Serena Scapucci +1
The vanishing of the Haantjes tensor is an important property that has been linked, for instance, to the existence of separation coordinates and the integrability of systems of hyd…
Symmetries and exact solutions of a reaction-diffusion system arising in population dynamics
Philip Broadbridge, Roman Cherniha, Vasyl' Davydovych +1
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible…
Cubic algebras, induced representations and general solution of the exceptional Laguerre equation
Ian Marquette
We consider the case of exceptional Laguerre polynomials of type I, II and III, their ordinary differential equations and the problem of finding general solution beside the p…
Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields
Pengcheng Lu, Junpeng Cao, Wen-Li Yang +2
The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra symmetry. Applying the method, we derive the homogeneous ze…
Representations of quadratic Heisenberg-Weyl algebras and polynomials in the fourth Painlevé transcendent
Ian Marquette
We provide new insights into the solvability property of an Hamiltonian involving of the fourth Painlevé transcendent and its derivatives. This Hamiltonian is third order shape inv…
Polynomial Poisson Algebras and Superintegrable Systems from Cartan centralisers of Types , and
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette +2
In this work, we construct explicit formulas for the generators of the Cartan centralisers of complex semisimple Lie algebras and , the case being already know…