Hunting of the quarton

Abstract

A summary is given of some of the author's results concerning the “CS equations” (C: Congruent S: Schroedinger operators) and the “ACS eqs.” (A: Altered). The CS eqs., respectively ACS eqs. are strongly 2+1-D (two spatial dimensions in addition to time) generalizations of the cornerstone (higher order) Korteweg-de Vries (KdV) eqs.,respectively IMKdV eqs. (I: Integrated, M: Modified) of soliton theory. The operator theoretic context which engenders the CS eqs. and the ACS eqs. is developed. The key to the relation between the CS eqs. and the ACS eqs. is either of the presented semifactorizations of the 2-D Schroedinger operator with potential function. Semifactorizations of the 4-D and 8-D Schroedinger operator are also achieved. Topics for further research are delineated.