Three problems of dynamics of solitons in Nonlinear Schrödinger Equation in presence of a strong nonlinearity
In this paper we analyze the formation, the stability, concentration properties of solitons (stable solitary waves) for the Nonlinear Schrödinger Equation when a strong nonlinearity is present.
We prove that, when the nonlinearity is sufficiently strong the dynamics of the soliton mimics the dynamics of a point particle in presence of an external potential. The proof will be given both in the confining potential and in the bounded potential case, using two different techniques. In the end, we will discuss the case of a singular potential.