The generalization of the addition property for soliton type processes

Abstract

A generalization of the addition relation for the Riemann theta functions and its limiting version for exponential functions appearing in soliton type equations are reported. The presented form seems to be particularly useful when processes in N+1, (N>1) space-time are analyzed. The commonly applied bilinear and trilinear approaches, restricted to the pure soliton processes, represent particular cases of the reported formalism. As an example, the dispersion equation for either quasiperiodic or soliton processes following 2+1 Calogero-Bogoyavlenskij-Schiff equation is derived.