Soliton solutions for fractional Schrödinger equations

Soliton Solutions for Quasilinear Schrödinger Equations

Soliton interactions in perturbed nonlinear Schrödinger equations.

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schrödinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the oth...

Soliton Dynamics for Fractional Schrödinger Equations

We investigate the soliton dynamics for the fractional nonlinear Schrödinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.

Soliton stability criterion for generalized nonlinear Schrödinger equations.

A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)<0 is a sufficient condition for instability, while p'(v)>0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximatel...

Soliton Solutions for Quasilinear Schrödinger Equations, I

For a class of quasilinear Schrödinger equations we establish the existence of ground states of soliton type solutions by a minimization argument.