109 citations · 383 across the 12 of their papers we have counts for
9 papers · 1 filter
Bright Fractional Single and Multi-Solitons in a Prototypical Nonlinear Schr{ö}dinger Paradigm: Existence, Stability and Dynamics
Robert J. Decker, A. Demirkaya, T. J. Alexander +1
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{ö}dinger equation. Motivated by the recent experimental…
Fractional Solitons: A Homotopic Continuation from the Biharmonic to the Harmonic Model
Robert J. Decker, A. Demirkaya, T. J. Alexander +2
In the present work we explore the path from a harmonic to a biharmonic PDE of Klein-Gordon type from a continuation/bifurcation perspective. More specifically, we make use of the…
Kink-Antikink Interaction Forces and Bound States in a nonlinear Schr{ö}dinger Model with Quadratic and Quartic dispersion
G. A. Tsolias, Robert J. Decker, A. Demirkaya +3
In the present work we explore the competition of quadratic and quartic dispersion in producing kink-like solitary waves in a model of the nonlinear Schr{ö}dinger type bearing cubi…
Dark solitons under higher order dispersion
Tristram J. Alexander, G. A. Tsolias, A. Demirkaya +3
We show theoretically that dark solitons can exist in the presence of pure quartic dispersion, and also in the presence of both quadratic and quartic dispersive effects, displaying…
Kink-Antikink Interaction Forces and Bound States in a Model with Quadratic and Quartic dispersion
G. A. Tsolias, Robert J. Decker, A. Demirkaya +2
We consider the interaction of solitary waves in a model involving the well-known Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different pref…
Kink-Antikink Interaction Forces and Bound States in a Biharmonic Model
Robert J. Decker, A. Demirkaya, N. S. Manton +1
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied Klein-Gordon theory. Specifically, we calculate the force between a well sepa…
Kink Dynamics in a Nonlinear Beam Model
Robert J. Decker, Aslihan Demirkaya, Panayotis G. Kevrekidis +3
In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key chara…
Kink Dynamics in a Parametric System: A Model With Controllably Many Internal Modes
A. Demirkaya, R. Decker, P. G. Kevrekidis +2
We explore a variant of the model originally proposed in Phys.\ Rev.\ D {\bf 12}, 1606 (1975) as a prototypical, so-called, "bag" model in which domain walls play the role of…
Spectral stability analysis for standing waves of a perturbed Klein-Gordon equation
Aslihan Demirkaya, Panayotis G. Kevrekidis, Milena Stanislavova +1
In the present work, we introduce a new -symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class…