91 citations · 1.2k across the 114 of their papers we have counts for
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Subalgebras of integrals, commutants, and superintegrable deformations of Lotka-Volterra systems
Ian Marquette, Peter H. van der Kamp, G. R. W. Quispel
We consider the Lie-algebraic notion of commutant in the setting of Poisson algebra. This provides a framework for deforming Hamiltonian differential equations. By taking a subalge…
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…
Algebraic approach and exact solutions of superintegrable systems in 2D Darboux spaces
Ian Marquette, Junze Zhang, Yao-Zhong Zhang
Superintegrable systems in 2D Darboux spaces were classified and it was found that there exist 12 distinct classes of superintegrable systems with quadratic integrals of motion (an…
Ground-state Bethe root densities and quantum phase transitions
Jon Links, Ian Marquette
Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe Ansatz equations, to identify quantum phase tran…
Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models
Ian Marquette, Jon Links
We study the Bethe Ansatz/Ordinary Differential Equation (BA/ODE) correspondence for Bethe Ansatz equations that belong to a certain class of coupled, nonlinear, algebraic equation…