Displaying similar documents to “Interaction of progressing waves through a nonlinear potential”

Caustics and wave front propagations: applications to differential geometry

Shyuichi Izumiya, Masatomo Takahashi (2008)

Banach Center Publications

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This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.

The wave map problem. Small data critical regularity

Igor Rodnianski (2005-2006)

Séminaire Bourbaki

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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....

On a theorem of Chekanov

Emmanuel Ferrand (1997)

Banach Center Publications

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A proof of the Chekanov theorem is discussed from a geometric point of view. Similar results in the context of projectivized cotangent bundles are proved. Some applications are given.