485 citations · 1.2k across the 29 of their papers we have counts for
29 papers
Characteristic approach to the soliton resolution
Piotr Bizoń, Bradley Cownden, Maciej Maliborski
As a toy model for understanding the soliton resolution phenomenon we consider a characteristic initial boundary value problem for the 4 equivariant Yang-Mills equation outside…
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…
Complex plane representations and stationary states in cubic and quintic resonant systems
Anxo Biasi, Piotr Bizon, Oleg Evnin
Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have construc…
A nonrelativistic limit for AdS perturbations
Piotr Bizon, Oleg Evnin, Filip Ficek
The familiar nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schroedinger equation, and the Einstein-massive-scala…
Solvable cubic resonant systems
Anxo Biasi, Piotr Bizon, Oleg Evnin
Weakly nonlinear analysis of resonant PDEs in recent literature has generated a number of resonant systems for slow evolution of the normal mode amplitudes that possess remarkable…
Two infinite families of resonant solutions for the Gross-Pitaevskii equation
Anxo Biasi, Piotr Bizon, Ben Craps +1
We consider the two-dimensional Gross-Pitaevskii equation describing a Bose-Einstein condensate in an isotropic harmonic trap. In the small coupling regime, this equation is accura…