Cauchy problem for dispersive equations
I have been interested in the local or global in time Cauchy problem in some Sobolev spaces for various dispersive equations in the class of non-linear Schrödinger equations coupled to matter equations. Some asymptotic limit equations have been investigated.
- Debye or Bloch matter in optics.
- Zakharov model for plasmas.
- Zozulya-Anderson model for photorefractive media.
I also studied a general framework for the Poisson’s recurrence for Hamiltonian equations and their numerical time discretizations.
- Journal papers: A-Bid95b
More recently I addressed the $p$-Schrödinger equation for the modelling of Newton’s cradle.
- Journal papers: A-BDJ13