3 papers
nlin.SI2025
Global branching of solutions to ODEs and integrability
Rod Halburd
We consider a natural generalisation of the Painlevé property and use it to identify the known integrable cases of the Lane-Emden equation with a real positive index. We classify…
math.CV2025
On the extension of analytic solutions of first-order difference equations
Rod Halburd, Risto Korhonen, Yan Liu +1
We will consider first-order difference equations of the form \[ y(z+1) = \frac{λy(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $λ\in\mathbb…
nlin.SI2024
All meromorphic solutions of a 3D Lotka-Volterra system: detecting partial integrability
Techheang Meng, Rod Halburd
For an autonomous system of ordinary differential equations, the existence of a meromorphic general solution is equivalent to the Painlevé property, which is widely used to detect…