Generalized KP Hierarchy for Several Variables

TL;DR

This paper extends the KP hierarchy to multiple variables, providing a new framework for solution classification and algebraic solution construction in integrable systems.

Contribution

It introduces a generalized KP hierarchy for several variables and offers methods for classifying and constructing algebraic solutions.

Findings

Proposes a multi-variable generalization of the KP hierarchy.

Provides a classification approach for solutions.

Develops a method to construct algebraic solutions.

Abstract

Following the techniques of M. Sato (see \cite{Sa}), a generalization of the KP hierarchy for more than one variable is proposed. An approach to the classification of solutions and a method to construct algebraic solutions is also offered.