Existence of exponentially and superexponentially spatially localized breather solutions for nonlinear klein–gordon lattices in ℤd, d ≥ 1

Autor: Dirk Hennig, Nikos I. Karachalios

Publikováno v: Proceedings of the Edinburgh Mathematical Society. 65:480-499

We prove the existence of exponentially and superexponentially localized breather solutions for discrete nonlinear Klein–Gordon systems. Our approach considers $d$-dimensional infinite lattice models with general on-site potentials and interaction

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f59ffb900027e05ebb076fff303ae9c1
https://doi.org/10.1017/s0013091522000189

The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation

Autor: Dirk Hennig, Nikos I. Karachalios, Jesús Cuevas-Maraver

Publikováno v: idUS. Depósito de Investigación de la Universidad de Sevilla
instname

While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger 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: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::599449f5c61a90e9cac3befe5a135813

Collapse dynamics for the discrete nonlinear Schrödinger equation with gain and loss

Autor: Nikos I. Karachalios, K. Vetas, Georgios Fotopoulos, V. Koukouloyannis

Publikováno v: Communications in Nonlinear Science and Numerical Simulation. 72:213-231

We discuss the finite-time collapse, also referred as blow-up, of the solutions of a discrete nonlinear Schrödinger (DNLS) equation incorporating linear and nonlinear gain and loss. Such an extended DNLS system appears in many inherently discrete ph

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30fc5eba5d12c57c8aa9711c35327993
https://doi.org/10.1016/j.cnsns.2018.12.016

Dynamics of a Higher-Order Ginzburg–Landau-Type Equation

Autor: Theodoros P. Horikis, Dimitrios J. Frantzeskakis, Nikos I. Karachalios

Publikováno v: Nonlinear Analysis, Differential Equations, and Applications ISBN: 9783030725624

We study possible dynamical scenarios associated with a higher-order Ginzburg–Landau-type equation. In particular, first we discuss and prove the existence of a limit set (attractor), capturing the long-time dynamics of the system. Then, we examine

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::23d6b503d122a3a21d33eaae3e39255b
https://doi.org/10.1007/978-3-030-72563-1_9

Kuznetsov–Ma breather-like solutions in the Salerno model

Autor: Nikos I. Karachalios, Panayotis G. Kevrekidis, Jesús Cuevas-Maraver, J. Sullivan, Efstathios G. Charalampidis

Publikováno v: idUS. Depósito de Investigación de la Universidad de Sevilla
instname
idUS: Depósito de Investigación de la Universidad de Sevilla
Universidad de Sevilla (US)

The Salerno model is a discrete variant of the celebrated nonlinear Schr¨odinger (NLS) equation interpolating between the discrete NLS (DNLS) equation and completely integrable Ablowitz-Ladik (AL) model by appropriately tuning the relevant homotopy

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc61076b106ca6f9ebeb73f7347e4a86
https://doi.org/10.1140/epjp/s13360-020-00596-1