Numerical study of 2+1 dimensional sine-Gordon solitons

Mesons, baryons and waves in the baby Skyrmion model

“…On the other hand the asymptotic behaviour of the ∞ energy anti-Skyrmion-like solution corresponding to (n = 1, m = 2, l = 1) is given by 9) where C and γ are constants. As the energy of these solutions is infinite we will not discuss them further in this paper and so we will always assume that l = 0 in what follows.…”

Nontopological Structures in the Baby-Skyrme Model

“…As this solution seemed very similar to the pulsons observed by [7] we have decided to look at it in more detail.…”

“…This equation has already been studied in [7], where it was shown that it had time dependent solutions similar to a breather, but which radiate their energy and slowly die out. The authors of [7] called such configurations pulsons.…”

“…Radial field configurations of (5) radiate relatively quickly when their amplitude of oscillation is relatively small, ie when the value of f never becomes larger than π/2 at the origin (these are the pulsons studied in [7].) However, when the amplitude of oscillation is larger than π/2 the general field configuration radiates its energy very slowly asymptotically reducing the amplitude of oscillation to a value a little larger than π/2 and settles at a pseudo-breather with a period of oscillation T ∼ 20.5 (when µ 2 = 0.1).…”

A matrix-based numerical method for the simulation of the two-dimensional sine-Gordon equation,

“…134], [11], [17], [18], [10], etc.). Despite using different techniques, the authors do not compare their methods; and their results for the test problems taken from [6] look very similar. On the other hand, in a recently submitted paper [9] (which can be obtained on request), F. de la Hoz and F. Vadillo have developed a pseudo-spectral matrix-based method to solve numerically SGE over an axiparallel rectangular domain in an arbitrary number of spatial dimensions, and with arbitrary time-dependent Neumann boundary conditions.…”