Global existence and compact attractors for the discrete nonlinear Schrödinger equation NI Karachalios, AN Yannacopoulos Journal of Differential Equations 217 (1), 88-123, 2005 | 90 | 2005 |

Existence of a global attractor for semilinear dissipative wave equations on RN NI Karachalios, NM Stavrakakis journal of differential equations 157 (1), 183-205, 1999 | 85 | 1999 |

On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence NI Karachalios, NB Zographopoulos Calculus of Variations and Partial Differential Equations 25 (3), 361-393, 2006 | 51 | 2006 |

Global existence and blow-up results for some nonlinear wave equations on {} NI Karachalios, NM Stavrakakis Advances in Differential Equations 6 (2), 155-174, 2001 | 51 | 2001 |

Convergence towards attractors for a degenerate Ginzburg-Landau equation NI Karachalios, NB Zographopoulos Zeitschrift für angewandte Mathematik und Physik ZAMP 56 (1), 11-30, 2005 | 43 | 2005 |

A remark on the existence of breather solutions for the discrete nonlinear Schrödinger equation in infinite lattices: the case of site-dependent anharmonic parameters NI Karachalios Proceedings of the Edinburgh Mathematical Society 49 (1), 115-129, 2006 | 31 | 2006 |

Thresholds for breather solutions on the Discrete Nonlinear Schr\" odinger Equation with saturable and power nonlinearity J Cuevas, JC Eilbeck, NI Karachalios arXiv preprint nlin/0609023, 2006 | 29 | 2006 |

Localized excitations in nonlinear complex systems R Carretero-González, J Cuevas-Maraver, D Frantzeskakis, ... Springer International Pu, 2016 | 27 | 2016 |

Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on NI Karachalios, NM Stavrakakis Discrete & Continuous Dynamical Systems-A 8 (4), 939, 2002 | 27 | 2002 |

Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves J Cuevas-Maraver, PG Kevrekidis, DJ Frantzeskakis, NI Karachalios, ... Physical Review E 96 (1), 012202, 2017 | 20 | 2017 |

Global attractor for the weakly damped driven Schrödinger equation in NI Karachalios, NM Stavrakakis Nonlinear Differential Equations and Applications NoDEA 9 (3), 347-360, 2002 | 18 | 2002 |

Asymptotic behavior of solutions of complex discrete evolution equations: the discrete Ginzburg-Landau equation NI Karachalios, HE Nistazakis, AN Yannacopoulos arXiv preprint math/0503297, 2005 | 17 | 2005 |

Global attractors and convergence to equilibrium for degenerate Ginzburg–Landau and parabolic equations NI Karachalios, NB Zographopoulos Nonlinear Analysis: Theory, Methods & Applications 63 (5-7), e1749-e1768, 2005 | 16 | 2005 |

Parametric exponential energy decay for dissipative electron-ion plasma waves NI Karachalios, NM Stavrakakis, P Xanthopoulos Zeitschrift für angewandte Mathematik und Physik ZAMP 56 (2), 218-238, 2005 | 16 | 2005 |

Asymptotic behavior of solutions of some nonlinearly damped wave equations on N Karachalios, N Stavrakakis Topological Methods in Nonlinear Analysis 18 (1), 73-87, 2001 | 14 | 2001 |

Escape dynamics in the discrete repulsive ϕ4 model V Achilleos, A Álvarez, J Cuevas, DJ Frantzeskakis, NI Karachalios, ... Physica D: Nonlinear Phenomena 244 (1), 1-24, 2013 | 13 | 2013 |

The number of bound states for a discrete Schrödinger operator on, lattices NI Karachalios Journal of Physics A: Mathematical and Theoretical 41 (45), 455201, 2008 | 12 | 2008 |

The semiflow of a reaction diffusion equation with a singular potential NI Karachalios, NB Zographopoulos manuscripta mathematica 130 (1), 63-91, 2009 | 11 | 2009 |

Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos V Achilleos, AR Bishop, S Diamantidis, DJ Frantzeskakis, TP Horikis, ... Physical Review E 94 (1), 012210, 2016 | 10 | 2016 |

Weyl’s type estimates on the eigenvalues of critical Schrödinger operators NI Karachalios Letters in Mathematical Physics 83 (2), 189-199, 2008 | 10 | 2008 |