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- Bartosz Bandrowski, Anna Karczewska, Piotr Rozmej
- Applied Mathematics and Computer Science
- 2010

This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a… (More)

The aim of the paper is to demonstrate the use of the Galerkin method for some kind of Volterra equations, determininistic and stochastic as well. The paper consists of two parts: the theoretical and numerical one. In the first part we recall some apparently well-known results concerning the Volterra equations under consideration. In the second one we… (More)

In the paper we study some numerical solutions to Volterra equations which interpolate heat and wave equations. We present a scheme for construction of approximate numerical solutions for one and two spatial dimensions. Some solutions to the stochastic version of such equations (for one spatial dimension) are presented as well.

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a… (More)

- W. Nörenberg, G. Pappand, P. Rozmej
- 2001

The diabatic approach to dissipative large-amplitude collective motion [1] is reformulated in a local energy-density approximation. We consider a general displacement field, which is defined by an expansion of the displacement potential in terms of multipoles, and include Coulomb interactions. This expansion allows the analytical evaluation of collective… (More)

We remind the properties of the intelligent (and quasi-intelligent) spin states introduced by Aragone et al. We use these states to construct families of coherent wave packets on the sphere and we sketch the time evolution of these wave packets for a rigid body molecule. The eigenstates of the square of the angular momentum operator L 2 which are also… (More)

- W Nörenberg, G Papp, P Rozmej
- 2008

The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of… (More)

- Anna Karczewska, Piotr Rozmej, Eryk Infeld
- Physical review. E, Statistical, nonlinear, and…
- 2014

An alternative way for the derivation of the new Korteweg-de Vries (KdV)-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It is obtained in the second-order perturbative approach in the weakly nonlinear, dispersive, and long… (More)

- Anna Karczewska, Piotr Rozmej, Eryk Infeld
- Physical review. E, Statistical, nonlinear, and…
- 2015

It is well known that the Korteweg-de Vries (KdV) equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum, and energy. Here we try to answer the question of how this comes about and also how these KdV quantities relate to those of the Euler shallow-water equations. Here Luke's Lagrangian is… (More)

- Anna Karczewska, Piotr Rozmej, Maciej Szczecinski, Bartosz Boguniewicz
- Applied Mathematics and Computer Science
- 2016