73 citations · 343 across the 31 of their papers we have counts for
12 papers · 1 filter
Existence theory for magma equations in dimension two and higher
David M. Ambrose, Gideon Simpson, J. Douglas Wright +1
We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar fie…
Local structure of singular profiles for a Derivative Nonlinear Schrödinger Equation
Yuri Cher, Gideon Simpson, Catherine Sulem
The Derivative Nonlinear Schrödinger equation is an -critical nonlinear dispersive equation model for Alfvén waves in space plasmas. Recent numerical studies on an -super…
Existence and Stability Properties of Radial Bound States for Schrödinger-Poisson with an External Coulomb Potential in Three Space Dimensions
Sarah Raynor, Jeremy L. Marzuola, Gideon Simpson
We consider radial solutions to the Schrödinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a model…
Petviashvilli's Method for the Dirichlet Problem
Derek Olson, Soumitra Shukla, Gideon Simpson +1
We examine the Petviashvilli method for solving the equation on a bounded domain with Dirichlet boundary conditions. We prove a local…
Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
Raphaël Côte, Claudio Muñoz, Didier Pilod +1
We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation ap…
Local Existence Theory for Derivative Nonlinear Schrödinger Equations with Non-Integer Power Nonlinearities
David M. Ambrose, Gideon Simpson
We study a derivative nonlinear Schrödinger equation, allowing non-integer powers in the nonlinearity, . Making careful use of the energy method, we are able to estab…