Computer two dimensional maps of loop soliton lattice systems using the new approach to the no integrability Aesthetic field equations

Abstract

We show that there are varieties of somewhat different loop soliton lattices when we specify an integration path in No Integrability Aesthetic Field Theory. These are illustrated using two dimensional computer maps. We have previously studied several such systems using the new approach to non-integrable systems developed in previous papers. [1-3]. The results of these earlier papers indicated that the solitons were rearranged by the new integration scheme in an erratic looking manner. However, we were restricted to regions close to the origin in these studies. With additional computer time made available and the use of tapes to store large amounts of information we have studied the above loop soliton systems and have been able to map considerable larger regions of the x, y plane. Symmetries for locations of the planar maxima and minima have been uncovered within a particular quadrant, although the symmetry found is not as great as the lattice. The type symmetry found is not maintained when more than one quadrant is involved. We also study a system that can be looked at as a perturbation of a loop lattice system. A brief discussion of the background material appears in the appendix.