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math.AP2026
Blow-up for the integrable defocusing Ablowitz-Ladik equation
Dirk Hennig, Nikos I. Karachalios, Dionyssios Mantzavinos +2
This work establishes finite-time blow-up for the completely integrable defocusing Ablowitz-Ladik equation on both infinite and finite lattices. We first establish local well-posed…
math.AP2025
Discrete Nonlinear Schrödinger versus Ablowitz-Ladik: Existence and dynamics of generalized focusing NLS-type lattices over a nonzero background
Dirk Hennig, Nikos I. Karachalios, Dionyssios Mantzavinos +1
The question of well-posedness of the generalized focusing Ablowitz-Ladik and Discrete Nonlinear Schrödinger equations with \textit{nonzero} boundary conditions on the infinite lat…