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arXiv · 2601.18211

Wave functions and k-point functions for the AKNS hierarchy

Ang Fu
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Abstract

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.

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Ang Fu. 2026-01-26. Wave functions and k-point functions for the AKNS hierarchy. https://arxiv.org/abs/2601.18211

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