Dynamical isoperimeter pattern in the square sine-Gordon system

Abstract

This paper shows by use of simple physical arguments the existence of a particular dynamical pattern in a---perturbed or not---two-dimensional sine-Gordon system. The stability of such modes is numerically checked. Their main topological invariant is the total length of the \ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi} wave fronts entering as elementary kinklike patterns the constitution of the whole configuration. This is consistent with the conservation of energy in all situations considered in this paper.