GEOMETRIC ASPECTS OF DEGENERATE MODULATION EQUATIONS
UNSPECIFIED (1994) GEOMETRIC ASPECTS OF DEGENERATE MODULATION EQUATIONS. STUDIES IN APPLIED MATHEMATICS, 91 (2). pp. 125-151. ISSN 0022-2526Full text not available from this repository.
Geometric aspects of degenerate modulation equations associated with spatially reversible systems are considered. Our primary observation is that stationary solutions of such equations always have a Poisson structure that is reminiscent of the equations governing the rigid body in mechanics. The Poisson structure is used to study the geometry of ''spatial'' phase space: A nontrivial Casimir of the Poisson structure provides a foliation of the phase space, spatially periodic states are given by critical points on level sets of the Casimir and stability type is given by the rate of change of the Casimir function. The bifurcation of spatially periodic states is then studied using singularity theory. The case where branches intersect transversely is treated in detail.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||STUDIES IN APPLIED MATHEMATICS|
|Number of Pages:||27|
|Page Range:||pp. 125-151|
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