Geometric methods in spectral theory of traveling waves and patterns
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Graham Cox
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Memorial University of Newfoundland
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Canada
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Yuri Latushkin
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University of Missouri
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USA
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Alim Sukhtayev
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Miami University
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USA
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Abstract:
| | We will bring together researchers working on various stability issues for such special solutions of partial differential equations as periodic and solitary waves. All aspects of stability/instability will be discussed, with a special emphasis on methods of spectral theory that lie at the heart of stability analyses. It will be expected of speakers that they will spend some time explaining the perspective underlying their work in order to stimulate further discussion and collaboration in the field.
A particular main theme will be applications of infinite dimensional symplectic geometry in the spectral theory of the operators obtained by linearizing the partial differential
equation about the traveling wave or other special solution. Specifically, we expect a number of talks to be concerned with the relation of the Maslov index, a topological invariant defined as the signed number of intersections of a path formed by Lagrangian subspaces with a train of a fixed subspace, and the Morse index counting the number of unstable eigenvalues of the linearization. Recently this topic has been the focus of attention of a large group of researchers, and a special session with this emphasis will foster further collaborations in this area. |
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List of approved abstract |
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