Nonlinear Schrödinger Equation for Superconductors

Nonlinear Schrödinger-helmholtz Equation as Numerical Regularization of the Nonlinear Schrödinger Equation

A regularized α−system of the Nonlinear Schrödinger Equation (NLS) with 2σ nonlinear power in dimension N is studied. We prove existence and uniqueness of local solution in the case 1 ≤ σ < 4 N−2 and existence and uniqueness of global solution in the case 1 ≤ σ < 4 N . When α → 0, this regularized system will converge to the classical NLS in the appropriate range. In particular, the purpose of ...

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity

Exact Moving Breather Solutions of a Generalized Discrete Nonlinear Schrödinger Equation

We obtain exact moving breather solutions of a generalized discrete nonlinear Schrödinger equation. For finite lattices, we find two different moving periodic breather solutions while for an infinite lattice we find a localized moving breather solution.

Coupled Nonlinear Schrödinger equation and Toda equation (the Root of Integrability)

We consider the relation between the discrete coupled nonlinear Schrödinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schrödinger equation. In the same way we can show the integrability in coupled case of dark and bright equations. Using this method we obtain several integrable equations.

The nonlinear Schrödinger equation with an inverse-square potential

We discuss recent results on the scattering/blow-up dichotomy below the ground state threshold for the focusing nonlinear Schrödinger equation with an inverse-square potential and a nonlinearity that is mass-supercritical and energy-subcritical.