Wave functions and k-point functions for the AKNS hierarchy

For an arbitrary solution to the AKNS hierarchy, the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method [14,21]. In this paper, we introduce a pair of wave functions of the solution and we use them to express the corresponding matrix resolvent. Based on this, we derive a new formula for the k-point correlation function of the AKNS hierarchy expressed in terms of wave functions. As an application, we show that the tau-function of an arbitrary solution to the AKNS hierarchy is a KP tau-function.

💡 Research Summary

The paper develops a new framework for the AKNS hierarchy by introducing a pair of formal wave functions and using them to express matrix resolvents and k‑point correlation functions. The authors begin by recalling the matrix‑resolvent (MR) method, which provides an efficient way to compute logarithmic derivatives of τ‑functions for integrable systems. For the AKNS hierarchy, the Lax operator L(ξ)=ε∂_X I+