Equations satisfied by a nine parameter subsystem obtained from mathematical aesthetic principles

摘要

We continue our study of equations obtained from a set of mathematically aesthetic principles. For a certain set of origin point data these equations collapse into a set of equations, called the ABJL equations, which describe sinusoidal behavior along any path segment. For another set of origin point data the equations collapse into a different set of equations, known as the ABMCHF equations, which describe sine within sine behavior along any path segment. More complicated origin point data lead to multiwave packet solutions. Here, we extend the three-dimensional sine within sine system to four dimensions in a simple way. Particular emphasis is placed on the study of the structure of the resulting equations. These equations we show have some resemblance to the Maxwell equations although there are important differences as well. This study suggests that even though the aesthetic equations do not on the surface resemble widely used equations a connection may exist on a more subtle level.