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math.AP2026
Instability of gray solitons in a Gross-Pitaevskii model with a moving impurity
Paolo Antonelli, Martino Caliaro
The effect of a moving impurity in a dilute Bose-Einstein condensate is investigated by means of the one-dimensional Gross-Pitaevskii model (GP) with non-zero boundary conditions a…
math.AP2026
On the Gross-Pitaevskii model with a moving impurity: Cauchy problem and superfluidity criterion
Paolo Antonelli, Martino Caliaro
We study the one-dimensional Gross-Pitaevskii equation with a traveling delta potential and non-zero conditions at infinity. This model describes the effect of a moving impurity in…
math.AP2026
Confinement and orbital stability of solitons of the NLS equation on metric graphs
Martino Caliaro, Diego Noja
We study the behavior of soliton states for the subcritical, time-dependent focusing NLS equation on a large family of non-compact metric graphs with Kirchhoff boundary conditions.…