-deformed bi-local fields. II.
-deformed KP hierarchy and -deformed constrained KP hierarchy.
Quantum Euler-Poisson systems: Existence of stationary states
A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small current densities. The proof is based on a reformulation of the dispersive third-order equation for the electron...
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quasi-periodic solutions of Hamiltonian PDEs
We overview recent existence results and techniques about KAM theory for PDEs.
Quasi-periodic solutions of nonlinear random Schrödinger equations
Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...