| 1. |
- Lundmark, Hans, 1970-
(författare)
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Formation and dynamics of shock waves in the Degasperis-Procesi equation
- 2007
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Ingår i: Journal of nonlinear science. - : Springer Science and Business Media LLC. - 0938-8974 .- 1432-1467. ; 17:3, s. 169-198
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Tidskriftsartikel (refereegranskat)abstract
- Solutions of the Degasperis-Procesi nonlinear wave equation may develop discontinuities in finite time. As shown by Coclite and Karlsen, there is a uniquely determined entropy weak solution which provides a natural continuation of the solution past such a point. Here we study this phenomenon in detail for solutions involving interacting peakons and antipeakons. We show that a jump discontinuity forms when a peakon collides with an antipeakon, and that the entropy weak solution in this case is described by a "shockpeakon" ansatz reducing the PDE to a system of ODEs for positions, momenta, and shock strengths.
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| 2. |
- Solari, HG, et al.
(författare)
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Minimal periodic orbit structure of 2-dimensional homeomorphisms
- 2005
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Ingår i: Journal of Nonlinear Science. - : Springer Science and Business Media LLC. - 0938-8974 .- 1432-1467. ; 15:3, s. 183-222
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Tidskriftsartikel (refereegranskat)abstract
- We present a method for estimating the minimal periodic orbit structure, the topological entropy, and a fat representative of the homeomorphism associated with the existence of a finite collection of periodic orbits of an orientation-preserving homeomorphism of the disk D-2. The method focuses on the concept of fold and recurrent bogus transition and is more direct than existing techniques. In particular, we introduce the notion of complexity to monitor the modification process used to obtain the desired goals. An algorithm implementing the procedure is described and some examples are presented at the end.
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