Majorations affines du nombre de zéros d'intégrales abéliennes pour les hamiltoniens quartiques elliptiques
Modulation of the Camassa-Holm equation and reciprocal transformations
We derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir of the second Poisson bracket of the KdV averaged flow. We show that the geometry...
Monopoles and modifications of bundles over elliptic curves.
Multi-component NLS models on symmetric spaces: spectral properties versus representations theory.