# St\"ackel transform of Lax equations

## TL;DR

This paper develops a method to generate Lax pairs for a broad class of St"ackel systems using the multi-parameter St"ackel transform, providing a parametrized family of solutions.

## Contribution

It introduces a systematic way to construct Lax pairs for St"ackel systems via the St"ackel transform, expanding the tools for integrability analysis.

## Key findings

- Constructed Lax pairs for various St"ackel systems.
- Parametrized Lax pairs by an arbitrary function.
- Enhanced understanding of integrability structures.

## Abstract

We construct Lax pairs for a wide class of St\"ackel systems by applying the multi-parameter St\"ackel transform to Lax pairs of a suitably chosen systems from the seed class. For a given St\"ackel system, the obtained set of non-equivalent Lax pairs is parametrized by an arbitrary function.