325 citations · 459 across the 11 of their papers we have counts for
13 papers
Three approaches to detecting discrete integrability
R. G. Halburd, R. J. Korhonen
A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in t…
Growth of meromorphic solutions of delay differential equations
Rod Halburd, Risto Korhonen
Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equation…
Bianchi permutability for the anti-self-dual Yang-Mills equations
Gregorio Benincasa, Rod Halburd
The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the ASDYM equations gener…
Height growth of solutions and a discrete Painlevé equation
A Al-Ghassani, R Halburd
Consider the discrete equation where the right side is of degree two in and where the coefficients , and…
All admissible meromorphic solutions of Hayman's equation
Rod Halburd, Jun Wang
We find all non-rational meromorphic solutions of the equation , where , and are rational functions of . In so doing we answer a questio…
Holomorphic curves with shift-invariant hyperplane preimages
Rodney Halburd, Risto Korhonen, Kazuya Tohge
If f: C -> P^n is a holomorphic curve of hyper-order less than one for which 2n + 1 hyperplanes in general position have forward invariant preimages with respect to the translation…