9 papers
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 Schröd…
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…
A new approach for the analysis of evolution partial differential equations on a finite interval
Türker Ãzsarı, 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…
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 la…
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…
Well-posedness of the higher-order nonlinear Schrödinger equation on a finite interval
Chris Mayo, Dionyssios Mantzavinos, Türker Ozsarı
We establish the local Hadamard well-posedness of a certain third-order nonlinear Schrödinger equation with a multi-term linear part and a general power nonlinearity known as the…