Scaling, self-similar solutions and shock waves for V-shaped field potentials

H. Arodå*, P. Klimas, T. Tyranowski

*Corresponding author for this work

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23 Citations (Scopus)
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Abstract

We investigate a (1+1) -dimensional nonlinear field theoretic model with the field potential V(Ï•)=â£Ï•â£. It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with an infinite number of degrees of freedom. We point out that the model has an interesting scaling symmetry. One consequence of that is the existence of self-similar solutions of the corresponding field equations. We also find discontinuous solutions of shock wave type.

Original languageEnglish
Article number046609
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Volume73
Issue number4
DOIs
Publication statusPublished - 2006
Externally publishedYes

Keywords

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