11 citations · 39 across the 12 of their papers we have counts for
12 papers
Stability of Breathers for a Periodic Klein-Gordon Equation
Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations…
The Dissipative Effect of Caputo--Time-Fractional Derivatives and its Implications for the Solutions of Nonlinear Wave Equations
Tassos Bountis, Julia Cantisán, Jesús Cuevas-Maraver +2
In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional diffe…
Breathers in the fractional Frenkel-Kontorova model
J. Catarecha, J. Cuevas-Maraver, P. G. Kevrekidis
In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically with space, inspired by the con…
On the proximity between the wave dynamics of the integrable focusing nonlinear Schrödinger equation and its non-integrable generalizations
Dirk Hennig, Nikos I. Karachalios, Dionyssios Mantzavinos +2
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…
Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach
F. Martin-Vergara, J. Cuevas-Maraver, P. E. Farrell +2
Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend…
Dissipative localised structures for the complex Discrete Ginzburg-Landau equation
Dirk Hennig, Nikos I. Karachalios, Jesús Cuevas-Maraver
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mech…