Trivially Related Lax Pairs Of The Sawada-Kotera Equation

TL;DR

This paper demonstrates that a recent Lax pair for the Sawada-Kotera equation is not new but trivially related to known Lax pairs, providing examples of trivial Lax pairs for KdV and Sawada-Kotera equations.

Contribution

It introduces the concept of trivial compositions of Lax pairs and shows how recent Lax pairs are related to known ones, clarifying their novelty.

Findings

The recent Lax pair for Sawada-Kotera is trivially related to known pairs.

Examples of trivial Lax pairs for KdV and Sawada-Kotera are provided.

Trivial compositions can generate new Lax pairs from known ones.

Abstract

We show that a recently introduced Lax pair of the Sawada-Kotera equation is not a new one but is trivially related to the known old Lax pair. Using the so-called trivial compositions of the old Lax pairs with a differentially constrained arbitrary operators, we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.