We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, |ψ| ψx. In the L-supercritical regime, σ > 1, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schrödinger ...

In this paper, we first established a high-accuracy difference scheme for the time-fractional Schrödinger equation (TFSE), where factional term is described in Caputo derivative. We used L1-2-3 formula to approximate derivative, and fourth-order compact finite utilized discretizing spatial term. The unconditional stability convergence of maximum norm are proved. Finally, verified theoretical re...

We present a novel approach for solving the time-dependent Schrödinger equation (TDSE). The method we propose converts TDSE to an equivalent Volterra integral equation; introducing global Lagrange interpolation of integrand transforms linear system, which is then solved iteratively. In this paper, derive method, explore its performance on several examples, and discuss corresponding numerical de...

We deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time dependent potential.