# Integrable (3+1)-dimensional system with an algebraic Lax pair

## TL;DR

This paper introduces the first known integrable (3+1)-dimensional dispersionless system with a nonisospectral algebraic Lax pair, expanding the class of such integrable systems beyond previously known rational cases.

## Contribution

It presents a novel integrable (3+1)-dimensional system with an algebraic Lax pair, demonstrating greater diversity in nonisospectral Lax pairs for such systems.

## Key findings

- First example of algebraic nonisospectral Lax pair in (3+1)D
- Expands understanding of integrable dispersionless systems
- Shows algebraic dependence broadens integrable system classes

## Abstract

We present a first example of an integrable (3+1)-dimensional dispersionless system with nonisospectral Lax pair involving algebraic, rather than rational, dependence on the spectral parameter, thus showing that the class of integrable (3+1)-dimensional dispersionless systems with nonisospectral Lax pairs is significantly more diverse than it appeared before. The Lax pair in question is of the type recently introduced in [A. Sergyeyev, Lett. Math. Phys. 108 (2018), no. 2, 359-376, arXiv:1401.2122 ].