148 citations · 187 across the 25 of their papers we have counts for
30 papers
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…
Local well-posedness of the higher-order nonlinear Schrödinger equation on the half-line: the case of two boundary conditions
Aykut Alkın, Dionyssios Mantzavinos, Türker Özsarı
We prove the local Hadamard well-posedness of the higher-order nonlinear Schrödinger equation with negative dispersion coefficient on the half-line under nonzero Dirichlet and Neum…
Interface problems of mixed spatial order
Dionyssios Mantzavinos, Ravindra Pethiyagoda, Dave Smith
We solve interface problems on the line between various constant coefficient linear evolution partial differential equations. Our prototypical examples are the heat, linear Schrödi…
The "good" Boussinesq equation on the half-line with Robin boundary conditions
Shivani Agarwal, Dionyssios Mantzavinos
We prove the local Hadamard well-posedness of the ``good'' Boussinesq equation formulated on the half-line with nonzero Robin boundary conditions. These boundary data involve the D…
On the proximal dynamics between integrable and non-integrable members of a generalized Korteweg-de Vries family of equations
Nikos I. Karachalios, Dionyssios Mantzavinos, Jeffrey Oregero
The distance between the solutions to the integrable Korteweg-de Vries (KdV) equation and a broad class of non-integrable generalized KdV (gKdV) equations is estimated in appropria…
A new approach for the analysis of evolution partial differential equations on a finite interval
Türker Özsarı, Dionyssios Mantzavinos, Konstantinos Kalimeris
We show that, for certain evolution partial differential equations, the solution on a finite interval can be reconstructed as a superposition of restrictions to $(0,\ell…