A dimension-breaking phenomenon in the theory of steady gravity-capillary water waves.Groves MD, Haragus M, Sun SM.
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK.
The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgassner in 1989. A model equation derived by B. B. Kadomtsev and V. I. Petviashvili in 1970 suggests that the Korteweg-de Vries line solitary wave belongs to a family of periodically modulated solitary waves which have a solitary-wave profile in the direction of motion and are periodic in the transverse direction. This prediction is rigorously confirmed for the full water-wave problem in the present paper. It is shown that the Korteweg-de Vries solitary wave undergoes a dimension-breaking bifurcation that generates a family of periodically modulated solitary waves. The term dimension-breaking phenomenon describes the spontaneous emergence of a spatially inhomogeneous solution of a partial differential equation from a solution which is homogeneous in one or more spatial dimensions.
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> 2) Some theories of quantum-electrodynamics in curved spacetime (one of the
> many not quite successful approaches to grand unified physics). In these
> theories, different observers in different reference frames may literally
> perceive different realities: a particle may be existent in one observer's
> reality, but nonexistent in another's. (This is a much stronger kind of
> relativity than one finds in special or general relativity theory proper.) Interesting, but it is still a defined subset of realities that can exist in
what I think of as the Universe or omniverse. In my meta-reality definition,
its purpose would be to derive sub-realities from it but designing them to
allow information to be translated from one reality to another.
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Ultra-hardcore total destruction now in a can, bottled and shipped outside of your region, buy now with limited edition Songs of the Seventies, faster faster faster, run till the sun goes red and the moon turns yellow!
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There Is No Gravity.
The Earth Sucks.
--Brett Easton Ellis