73 citations · 343 across the 31 of their papers we have counts for
4 papers · 1 filter
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…
Ill-posedness of degenerate dispersive equations
David M. Ambrose, Gideon Simpson, J. Douglas Wright +1
In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation…
Embedded Eigenvalues and the Nonlinear Schrodinger Equation
Reza Asad, Gideon Simpson
A common challenge to proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues…
Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation
Daniel Ginsberg, Gideon Simpson
We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an ele…