Multitime Rayleigh Solitons

Details Multitime Rayleigh Solitons Multitime Rayleigh Solitons

2011-10-13

arxiv.org/abs/1110.2889v1

Physics

Mathematical Physics

To create the multitime solitons we borrow geometrical objects from the jet bundle of order one (connections, vector fields, t

Scientific paper

Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and Bernoulli ODEs. These multitime solitons develop complex behavior of deformation phenomena. Section 1 presents the single-time Rayleigh wave equations. Section 2 analyzes the geometric characteristics (fundamental tensor, linear connection, vector fields, tensor fields) associated to the Rayleigh PDEs, showing the existence of an infinity of geometrical structures such that the multitime PDEs are prolongations of single-time PDE. Section 3 builds the ultra-parabolic-hyperbolic differential operator defining the multitime Rayleigh wave equations. Section 4 gives the technique capable to produce the multitime Rayleigh solitons. Sections 5 and 6 praise explicit formulas for the multitime Rayleigh solitons.

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