Zobrazeno 1 - 10
of 95
pro vyhledávání: '"Karachalios, Nikos I."'
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 context of the nonlinear physics of ecosystems, modelling the dynamics of
Externí odkaz:
http://arxiv.org/abs/2406.16598
Autor:
Fotopoulos, Georgios, Karachalios, Nikos I., Koukouloyannis, Vassilis, Kyriazopoulos, Paris, Vetas, Kostas
The study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with fascinating dyna
Externí odkaz:
http://arxiv.org/abs/2312.03683
Autor:
Hennig, Dirk, Karachalios, Nikos I., Mantzavinos, Dionyssios, Cuevas-Maraver, Jesus, Stratis, Ioannis G.
The question of whether features and behaviors that are characteristic to completely integrable systems persist in the transition to non-integrable settings is a central one in the field of nonlinear dispersive equations. In this work, we investigate
Externí odkaz:
http://arxiv.org/abs/2307.16408
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of survival/destruct
Externí odkaz:
http://arxiv.org/abs/2303.02383
Autor:
Hennig, Dirk, Karachalios, Nikos I.
We prove the existence of periodic travelling wave solutions for general discrete nonlinear Klein-Gordon systems, considering both cases of hard and soft on-site potentials. In the case of hard on-site potentials we implement a fixed point theory app
Externí odkaz:
http://arxiv.org/abs/2212.05575
Autor:
Hennig, Dirk, Karachalios, Nikos I., Mantzavinos, Dionyssios, Cuevas-Maraver, Jesús, Stratis, Ioannis G.
Publikováno v:
In Journal of Differential Equations 15 July 2024 397:106-165
The Ablowitz-Ladik system, being one of the few integrable nonlinear lattices, admits a wide class of analytical solutions, ranging from exact spatially localised solitons to rational solutions in the form of the spatiotemporally localised discrete P
Externí odkaz:
http://arxiv.org/abs/2105.04202
Autor:
Hennig, Dirk, Karachalios, Nikos I.
The problem of showing the existence of localised modes in nonlinear lattices has attracted considerable efforts from the physical but also from the mathematical viewpoint where a rich variety of methods has been employed. In this paper we prove that
Externí odkaz:
http://arxiv.org/abs/2105.00745
Autor:
Hennig, Dirk, Karachalios, Nikos I.
Discrete Ginzburg-Landau (DGL) equations with non-local nonlinearities have been established as significant inherently discrete models in numerous physical contexts, similar to their counterparts with local nonlinear terms. We study two prototypical
Externí odkaz:
http://arxiv.org/abs/2104.00338
Publikováno v:
Journal of Differential Equations (2022)
While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schr\"odinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a "continuous dependence"
Externí odkaz:
http://arxiv.org/abs/2102.05332