6 papers
Explicit higher order rational rogue waves of the nonlinear Schrödinger equation
Robert Conte, ENS Paris-Saclay, The University of Hong Kong
The -th order rational rogue wave of the nonlinear Schrödinger equation (NLS), which depends on real parameters, has been shown to be impossible to generate by the nonl…
On the Gurevich-Pitaevskii solution of KdV
Robert Conte
The universal solution of the Korteweg-de Vries equation (KdV) introduced by Gurevich and Pitaevskii in order to describe the onset of dispersive shock waves is known to also obey…
Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distribution
Ivan Dornic, Robert Conte
We determine the full persistence probability distribution for a non-Markovian stochastic process, motivated by first-passage questions arising in interacting spin systems and alli…
Holomorphic, rational Lax pairs of a -discrete Painlevé VI equation
Robert Conte
We build several matrix Lax pairs of valid even when the two eigenvalues of the residue of the monodromy matrix at infinity are equal. Their elements are ratio…
Minimal algebraic solutions of the sixth equation of Painlevé
Robert Conte
For each of the forty-eight exceptional algebraic solutions of the sixth equation of Painlevé, we build the algebraic curve of a degree conjectured to be minimal…
Methods for exact solutions of nonlinear ordinary differential equations\
Robert Conte, Micheline Musette, Tuen Wai Ng +1
In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall cl…