23 citations · 51 across the 10 of their papers we have counts for
10 papers
Analysis and Simulations of a Nonlocal Gray-Scott Model
Loic Cappanera, Gabriela Jaramillo, Cory Ward
The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio…
Numerical Methods for a Diffusive Class Nonlocal Operators
Loic Cappanera, Gabriela Jaramillo, Cory Ward
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, , of diffusive type. I…
Rogue Waves and Periodic Solutions of a Nonlocal Nonlinear Schrödinger Model
C. B. Ward, P. G. Kevrekidis, T. P. Horikis +1
In the present work, a nonlocal nonlinear Schrödinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations, by consider…
Rogue Waves as Self-Similar Solutions on a Background: A Direct Calculation
C. B. Ward, P. G. Kevrekidis
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schrödinger equation, but…
Solitary Waves of the Camassa-Holm Derivative Nonlinear Schrödinger equation
L. J. Guo, C. B. Ward, I. K. Mylonas +1
In this paper we examine a deformation of the derivative nonlinear Schrödinger (DNLS) equation, the so-called Camassa-Holm DNLS (CH-DNLS) equation. We use two asymptotic multiscale…
Solitary Waves of the Two-Dimensional Camassa-Holm--Nonlinear Schrödinger Equation
C. B. Ward, I. K. Mylonas, P. G. Kevrekidis +1
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schrödinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We us…