Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies

TL;DR

This paper explicitly constructs squared eigenfunction symmetries for the BTL and CTL hierarchies, linking them to additional symmetries and extending the understanding of integrable systems.

Contribution

It introduces explicit constructions of squared eigenfunction symmetries for BTL and CTL hierarchies, connecting them to additional symmetries.

Findings

Squared eigenfunction symmetries are explicitly constructed for BTL and CTL hierarchies.

These symmetries are shown to generate additional symmetries.

The connections between eigenfunction symmetries and the hierarchy constraints are clarified.

Abstract

In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are explicitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and CTL constraints. Also the connections with the corresponding additional symmetries are investigated: the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries.