4 problems

Consider a discrete nonlinear Schrödinger equation on a lattice, with localized modes or discrete breathers understood as periodic-in-time and spatially localized solutions. A latt…

Let the discrete nonlinear Schrödinger equation with saturation be … where $h$ is the lattice spacing and $\theta$ is the saturation parameter. Consider the transparent points for…

Nonexistence conjecture. If $H$ has more than three eigenvalues, then there will be no quasi-periodic solution of this form.

Consider the discrete nonlinear Schrödinger evolution and its soliton family $e^{-i(-\mu t+\nu)}\alpha_\mu$, parametrized by $(\mu,\nu)$. The associated soliton manifold is the set…