Antonio Moro
(Dipartimento di Fisica - Univ. Lecce)
Dispersionless Veselov-Novikov hyerarchy in nonlinear geometrical optics and hydrodynamic-type reductions
We introduce nonlocal nonlinear Schroedinger equation to describe the propagation of a laser beam in a medium which exhibits different degrees of nonlocality. We show that in high frequency limit, under suitable phenomenological assumptions, this system is described by the dispersionless Veselov-Novikov hierarchy. Each equation of the hierarchy corresponds to a specific degree of nonlocality. The problem of compatibility with a general class of nonlinear response of physical interest is also discussed. A reduction method based on symmetry constraints is used to construct hydrodynamic type reductions which are compatible with the class of nonlinear responses considered.