In this paper, we implement the Adaptive Moving Mesh method (AMM) to solution of initial value problems involving Schr\"odinger equation, and more specifically Schr\"odinger-Poisson system equations. This is based on problem a discrete domain, whose resolution coordinate time-dependent, allows dynamically assign numerical in terms desired refinement criteria. We apply solve various test station...

The Meta-Schr\"odinger algebra arises as the dynamical symmetry in transport processes which are ballistic a chosen `parallel' direction and diffusive all other `transverse' directions. time-space transformations of this Lie its infinite-dimensional extension, meta-Schr\"odinger-Virasoro algebra, constructed. We also find representation suitable for non-stationary systems by proposing generalis...

many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. for the efficient solution of the above mentioned problems, linear multistep methods or runge-kutta technique are used. for the simulation of chemical procedures the ra...

We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs forced version of this equation. The forcing consists terms involving quadratic products certain eigenfunctions the associated Lax pair. Remarkably, some these equations arise modelling important physical phenomena. initial value problem can be formulated as Riemann-Hilbe...