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Level sets as progressing waves: an example for wake-free waves in every dimension
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The potential energy surface of a molecule can be decomposed into equipotential hypersurfaces of the level sets. It is a foliation. The main result is that the contours are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The energy seen as an additional coordinate plays the central role in this treatment. A solution of the wave equation can be a sharp front in the form of a delta distribution. We discuss a general Huygens' principle: there is no wake of the wave solution in every dimension.
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QUAPP, Wolfgang and BOFILL I VILLÀ, Josep M. Level sets as progressing waves: an example for wake-free waves in every dimension. Journal of Mathematical Chemistry. 2013. Vol. 52, num. 2, pags. 654-664. ISSN 0259-9791. [consulted: 20 of August of 2026]. Available at: https://hdl.handle.net/2445/152916