# Multi-component generalizations of mKdV equation and non-associative algebraic structures

## TL;DR

This paper explores the connection between algebraic structures like triple Jordan systems and integrable multi-component mKdV models, revealing new algebraic frameworks such as Lie-Jordan algebras.

## Contribution

It introduces a general multi-component mKdV model linked to triple Jordan systems and skew-symmetric operations, expanding the algebraic understanding of integrable systems.

## Key findings

- Established relations between triple Jordan systems and multi-component mKdV models
- Identified the role of Lie brackets in forming Lie-Jordan algebras
- Provided a unified algebraic framework for integrable multi-component equations

## Abstract

Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric bilinear operation. If this operation is a Lie bracket, then we arrive at the Lie-Jordan algebras