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dc.contributor.authorBeck, Margaret A.en_US
dc.contributor.authorLatushkin, Yurien_US
dc.contributor.authorCox, Grahamen_US
dc.contributor.authorMcquighan, Kellyen_US
dc.contributor.authorJones, Christopheren_US
dc.contributor.authorSukhtayev, Alimen_US
dc.date2017-08-22
dc.date.accessioned2018-02-12T19:08:49Z
dc.date.available2018-02-12T19:08:49Z
dc.identifier.citationMA Beck, Yuri Latushkin, Graham Cox, Kelly Mcquighan, Christopher Jones, Alim Sukhtayev. "Instability of pulses in gradient reaction-diffusion systems: a symplectic approach." Philosophical Transactions A: Mathematical, Physical and Engineering Sciences,
dc.identifier.issn1364-503X
dc.identifier.urihttps://hdl.handle.net/2144/26963
dc.description.abstractIn 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.en_US
dc.publisherRoyal Society, Theen_US
dc.relation.ispartofPhilosophical Transactions A: Mathematical, Physical and Engineering Sciences
dc.subjectMathematical physicsen_US
dc.subjectClassical analysis and ODEsen_US
dc.subjectDynamical systemsen_US
dc.titleInstability of pulses in gradient reaction-diffusion systems: a symplectic approachen_US
dc.typeArticleen_US
dc.identifier.doi10.1098/rsta.2017.0187
pubs.elements-sourcemanual-entryen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusAccepteden_US


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