46 citations · 176 across the 42 of their papers we have counts for
43 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…
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…
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…
Persistence of integrable wave dynamics in the Discrete Gross--Pitaevskii equation: the focusing case
G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis
Expanding upon our prior findings on the proximity of dynamics between integrable and non-integrable systems within the framework of nonlinear Schrödinger equations, we examine thi…
On the proximity of Ablowitz-Ladik and discrete Nonlinear Schrödinger models: A theoretical and numerical study of Kuznetsov-Ma solutions
Madison L. Lytle, Efstathios G. Charalampidis, Dionyssios Mantzavinos +3
In this work, we investigate the formation of time-periodic solutions with a non-zero background that emulate rogue waves, known as Kuzentsov-Ma (KM) breathers, in physically relev…
Nonlinear lattices from the physics of ecosystems: The Lefever-Lejeune nonlinear lattice in
Nikos I. Karachalios, Antonis Krypotos, Paris Kyriazopoulos
We argue that the spatial discretization of the strongly nonlinear Lefever-Lejeune partial differential equation defines a nonlinear lattice that is physically relevant in the cont…