Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-10-24
Acta Phys.Polon. B36 (2005) 3861-3876
Physics
High Energy Physics
High Energy Physics - Theory
Presented at the XLV Cracow School of Theoretical Physics, Zakopane, Poland, June 2005. 18 pages, 6 .eps figures. To appear in
Scientific paper
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground state value of the field is achieved on a finite distance - there are no exponential tails. This applies in particular to soliton-like object called the topological compacton. Next, we discuss scaling invariance which appears when the fields are restricted to small amplitude perturbations of the ground state. Evolution of such perturbations is governed by nonlinear equation with a non-smooth term which can not be linearized even in the limit of very small amplitudes. Finally, we briefly describe self-similar and shock wave solutions of that equation.
Arodz Henryk
Klimas Pawel
Tyranowski T.
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