# A New form of Kr\"onecker product-Lax pair and coupled systems

## TL;DR

This paper introduces a novel approach to generate nonlinear integrable systems using a new form of Kronecker product combined with Lax pairs, highlighting their bi-Hamiltonian structure and providing explicit examples.

## Contribution

It presents a new method for constructing integrable systems via a modified Kronecker product and Lax pairs, expanding the toolkit for studying nonlinear integrable equations.

## Key findings

- Generated new integrable systems with bi-Hamiltonian structure
- Provided explicit examples of the new equations
- Demonstrated the method's effectiveness in producing known and novel systems

## Abstract

A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure. Actually they are all bi-Hamiltonian. A few explicit form of such equations are given also