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math.AP2025
On ill-posedness for the Gabitov--Turitsyn equation
Matthew Kowalski
We investigate the well- and ill-posedness theory for the Gabitov--Turitsyn equation, which models the long-time dynamics of pulses in dispersion-managed optical fibers. We identif…
math.AP2025
On dispersive decay for the generalized Korteweg--de Vries equation
Matthew Kowalski, Minjie Shan
We prove pointwise-in-time dispersive estimates for solutions to the generalized Korteweg--de Vries (gKdV) equation. In particular, for solutions to the mass-critical model, we ass…