73 citations · 343 across the 31 of their papers we have counts for
7 papers · 1 filter
Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation
Jeremy L. Marzuola, Sarah Raynor, Gideon Simpson
We study soliton solutions to a generalized Korteweg - de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of the authors for the nonlinear Schrödi…
Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation
Xiao Liu, Gideon Simpson, Catherine Sulem
We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability…
Broad Band Solitons in a Periodic and Nonlinear Maxwell System
Dmitry Pelinovsky, Gideon Simpson, Michael I. Weinstein
We consider the one-dimensional Maxwell equations with low contrast periodic linear refractive index and weak Kerr nonlinearity. In this context, wave packet initial conditions wit…
Coherent Structures and Carrier Shocks in the Nonlinear Periodic Maxwell Equations
Gideon Simpson, Michael I. Weinstein
We consider the one-dimensional propagation of electromagnetic waves in a weakly nonlinear and low-contrast spatially inhomogeneous medium with no energy dissipation. We focus on t…
A system of ODEs for a Perturbation of a Minimal Mass Soliton
J. Marzuola, S. Raynor, G. Simpson
We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a…
On a Hamiltonian PDE arising in Magma Dynamics
Gideon Simpson, Michael I. Weinstein, Philip Rosenau
In this article we discuss a new Hamiltonian PDE arising from a class of equations appearing in the study of magma, partially molten rock, in the Earth's interior. Under physically…