3 citations · 8 across the 4 of their papers we have counts for
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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…
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…
Asymptotic Stability of Ascending Solitary Magma Waves
Gideon Simpson, Michael I. Weinstein
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is fou…