3 papers
math.AP2023
Ground state of the Gross-Pitaevskii equation with a harmonic potential in the energy-critical case
Dmitry E. Pelinovsky, Szymon Sobieszek
Ground state of the energy-critical Gross-Pitaevskii equation with a harmonic potential can be constructed variationally. It exists in a finite interval of the eigenvalue parameter…
math-ph2020
Ground state in the energy super-critical Gross-Pitaevskii equation with a harmonic potential
Piotr Bizon, Filip Ficek, Dmitry E. Pelinovsky +1
The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to p…
math.DS2020
A qualitative study of an anaerobic food-web reveals the importance of hydrogen for microbial stability
Szymon Sobieszek, Gail S. K. Wolkowicz, Matthew J. Wade
The mathematical analysis of a three-tiered food-web describing anaerobic chlorophenol mineralisation has suggested the emergence of interesting dynamical behaviour through its spe…