Displaying similar documents to “Addendum to a paper of Craig and Goodman.”

Space-time caustics.

Gorman, Arthur D. (1986)

International Journal of Mathematics and Mathematical Sciences

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Time-evolution of a caustic.

Ari, Nasit, Gorman, Arthur D. (1988)

International Journal of Mathematics and Mathematical Sciences

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On caustics associated with Rossby waves

Arthur D. Gorman (1996)

Applications of Mathematics

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Rossby wave equations characterize a class of wave phenomena occurring in geophysical fluid dynamics. One technique useful in the analysis of these waves is the geometrical optics, or multi-dimensional WKB technique. Near caustics, e.g., in critical regions, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to study Rossby waves near caustics.

On caustics associated with the linearized vorticity equation

Petya N. Ivanova, Arthur D. Gorman (1998)

Applications of Mathematics

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The linearized vorticity equation serves to model a number of wave phenomena in geophysical fluid dynamics. One technique that has been applied to this equation is the geometrical optics, or multi-dimensional WKB technique. Near caustics, this technique does not apply. A related technique that does apply near caustics is the Lagrange Manifold Formalism. Here we apply the Lagrange Manifold Formalism to determine an asymptotic solution of the linearized vorticity equation and to study...

Smooth optimal synthesis for infinite horizon variational problems

Andrei A. Agrachev, Francesca C. Chittaro (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification...