3 papers
math.AP2026
Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system
Michał Kowalczyk, Jarosław Mederski, Isidora Miranda
We consider a one-dimensional coupled defocusing Schrödinger system with a nonzero background in its first component and finite mass in its second component. We prove global well-p…
math.AP2025
Asymptotic analysis of small energy breathers for the nonlinear Klein-Gordon equation
Michał Kowalczyk, Yvan Martel
For a class of nonlinear Klein-Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulate…
math.AP2025
A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation
Michał Kowalczyk, Yvan Martel
The asymptotic stability of the black and dark solitons of the one-dimensional Gross-Pitaevskii equation was proved by Béthuel, Gravejat and Smets (Ann. Sci. Éc. Norm. Supér. 48 (2…