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• W3100992070 endingPage "20170187" @default.
• W3100992070 startingPage "20170187" @default.
• W3100992070 abstract "In a scalar reaction-diffusion equation, it is known that the stability of a steady state can be determined from the Maslov index, a topological invariant that counts the state's critical points. In particular, this implies that pulse solutions are unstable. We extend this picture to pulses in reaction-diffusion systems with gradient nonlinearity. In particular, we associate a Maslov index to any asymptotically constant state, generalizing existing definitions of the Maslov index for homoclinic orbits. It is shown that this index equals the number of unstable eigenvalues for the linearized evolution equation. Finally, we use a symmetry argument to show that any pulse solution must have nonzero Maslov index, and hence be unstable." @default.
• W3100992070 created "2020-11-23" @default.
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• W3100992070 date "2018-03-05" @default.
• W3100992070 modified "2023-10-06" @default.
• W3100992070 title "Instability of pulses in gradient reaction–diffusion systems: a symplectic approach" @default.
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• W3100992070 doi "https://doi.org/10.1098/rsta.2017.0187" @default.
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