8 papers
Solitary waves and vortices in a Nonlinear Schrödinger equation with ponderomotive nonlinearity
D. K. Campbell, J. Cuevas-Maraver, R. Goh +1
In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of…
Dark solitons in the fractional NLS equation
Almudena P. Márquez, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis
In the present work we consider the subject of dark fractional solitary waves in the realm of generalized (fractional) forms of the nonlinear Schrödinger (NLS) equation. While ear…
On the Fractional Dynamics of Kinks in sine-Gordon Models
T. Bountis, J. Cantisán, J. Cuevas-Maraver +2
In the present work we explore the dynamics of single kinks, kink-anti-kink pairs and bound states in the prototypical fractional Klein-Gordon example of the sine-Gordon equation.…
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…
Standing and Traveling Waves in a Nonlinearly Dispersive Lattice Model
Ross Parker, Pierre Germain, Jesús Cuevas-Maraver +2
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schrödinger equa…
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…