Eminence Of Solitons

A soliton is a tense of a wave-packet.  In the case of a very microscopic tense (at the Ward-Cauchy level), such a wave-packet is to only happen, when the Ricci Curvature is flat. Before I go further with this discussion; try to keep in mind, that we are about to discuss a basic relationship, that is here to exist between two different general types of wave-fronts, that are here to be directly correlative to each other in a viable manner, at the same general locus, -- and these two different types of wave-fronts are:  1) The actual wave-front of the soliton itself; and, 2) The wave-front of the gravitational energy, that is here to be transferred/translated through the general region, at which the actual soliton is to be eminent at, over what will here tend to be a relatively brief amount of extrapolated time.;  Here we go with the rest of the topic!: The Ricci Curvature is flat, when the net wavelengths of those particular gravity waves, that are here to be translated through the general region, at which such a directly associated type of a wave-packet is thence to exist, are here to bear a net wavelength of zero, -- even though the general tense of a cotangent bundle, of which is here to act as the holonomic substrate of such a said wave-packet, is obviously to work to bear its own tense of a viable wavelength, at a level that is to be basically Poincare to the topological surface of the inferred packet of wave-like phenomenology.  The more pronounced that the reverse-nodal behavior is to be, of those particular Schwinger-Indices, that are here to be propagated in a manner, that is to bear the nature of being of both a transversal and of a perpendicular manner, over time, for what is here to work to help at allowing for the physical conditions of such a tense of a soliton to exist, at a relatively microscopic level -- to where such a general tense of a wave-packet of discrete energy eigenstates, are here to be facilitated into such a tense of activity, by the inferred general characteristic of those implied directly associated gravitational waves, that are here to work to cancel each others' wavelengths at the same general proximal local region at which the stated soliton is here to be formed (even though, certainly, the actual force of gravity that is to be propagated through such a general region of space, in and of itself, is here to tend to be spontaneously translated outward  from such a region, in the meanwhile), to where, in the process of working to form the proximal local presence of a soliton-related Ward-Cauchy-based configuration, at the general locus at which the inferred condition of a flat Ricci Curvature is here to be present, by which this tendency will work here to allow for the consequential wave-like characteristics of the said soliton-like construct to resultantly occur as such, -- to where the presence of such a said soliton, will then consequently tend to be more eminent than otherwise. To Be Continued! Sincerely, Sam Roach.