The structure of rationally factorized Lax type flows and their analytical integrability

TL;DR

This paper develops a broad class of integrable differential-functional systems with rich algebraic structures, focusing on operator Lax equations for factorized seed elements and providing an analytical solution scheme.

Contribution

It introduces a new framework for analyzing Lax type flows with rational factorization, including a key theorem on operator factorization and solution methods.

Findings

Proved a theorem on operator factorization of Lax equations.

Developed an analytical solution scheme for the systems.

Established the integrability of a wide class of dynamical systems.

Abstract

The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type equations for factorized seed elements, there is proved an important theorem about their operator factorization and the related analytical solution scheme to the corresponding nonlinear differential-functional dynamical systems.