43 citations · 54 across the 4 of their papers we have counts for
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math.DS2017★ 43 cited
On the Existence and Stability of Fast Traveling Waves in a Doubly-Diffusive FitzHugh-Nagumo System
Paul Cornwell, Christopher K. R. T. Jones
The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as a paradigmatic activa…
math.DS2017★ 7 cited
Opening the Maslov Box for Traveling Waves in Skew-Gradient Systems
Paul Cornwell
We obtain geometric insight into the stability of traveling pulses for reaction-diffusion equations with skew-gradient structure. For such systems, a Maslov index of the traveling…
math.DS2017★ 4 cited
A Stability Index for Traveling Waves in Activator-Inhibitor Systems
Paul Cornwell, Christopher K. R. T. Jones
We consider the stability of nonlinear traveling waves in a class of activator-inhibitor systems. The eigenvalue equation arising from linearizing about the wave is seen to preserv…