30 citations · 85 across the 4 of their papers we have counts for
6 papers
Vortices, Painlevé integrability and projective geometry
Felipe Contatto
The first half of the thesis concerns Abelian vortices and Yang-Mills (YM) theory. It is proved that the 5 types of vortices recently proposed by Manton are symmetry reductions of…
Manton's five vortex equations from self-duality
Felipe Contatto, Maciej Dunajski
We demonstrate that the five vortex equations recently introduced by Manton ariseas symmetry reductions of the anti-self-dual Yang--Mills equations in four dimensions. In particula…
Integrable Abelian Vortex-like solitons
Felipe Contatto
We propose a modified version of the Ginzburg-Landau energy functional admitting static solitons and determine all the Painlevé-integrable cases of its Bogomolny equations of a giv…
Metrisability of Painlevé equations
Felipe Contatto, Maciej Dunajski
We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ODEs with Painlevé property, and determine for which of these equations thei…
First integrals of affine connections and Hamiltonian systems of hydrodynamic type
Felipe Contatto, Maciej Dunajski
We find necessary and sufficient conditions for a local geodesic flow of an affine connection on a surface to admit a linear first integral. The conditions are expressed in terms o…
Instanton Solutions from Abelian Sinh-Gordon and Tzitzeica Vortices
Felipe Contatto, Daniele Dorigoni
We study the Abelian Higgs vortex solutions to the sinh-Gordon equation and the elliptic Tzitzeica equation. Starting from these particular vortices, we construct solutions to the…