Sylvain Carpentier

collaborators

3 papers

math.AP2017

Compatible Hamiltonian Operators for the Krichever-Novikov Equation

Sylvain Carpentier

It has been proved by V. Sokolov that the Krichever-Novikov equation's hierarchy is hamiltonian for the non-local Hamiltonian operator H_0=u_x D^{-1} u_x and possesses twi weakly n…

math-ph2016

A sufficient condition for a Rational Differential Operator to generate an Integrable System

Sylvain Carpentier

For a rational differential operator $L = A B^{- 1}$ , the Lenard-Magri scheme of integrability is a sequence of functions $F_{n}, n \geq 0$ , such that (1) $B (F_{n + 1}) = A (F_{n})$ for all $n \…

math.AG2016

Tropical Embeddings of Metric Graphs

Adan Medrano Martin del Campo, Sylvain Carpentier

Every graph $Γ$ can be embedded in the plane with a minimal number of edge intersections, called its classical crossing number $cross (Γ)$ . In this paper, we prove…