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arXiv · 2603.08301

Constraints of the D$\Delta$KP hierarchy to the semi-discrete AKNS and Burgers hierarchies

Jin Liu·Da-jun Zhang
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Abstract

The paper investigates three eigenfunction constraints of two (2+1)-dimensional differential-difference integrable systems. First, we revisit the known squared eigenfunction symmetry constraint of the differential-difference Kadomtsev-Petviashvili (D$\Delta$KP) hierarchy, which gives rise to a semi-discrete Ablowitz-Kaup-Newell-Segur hierarchy. Second, we introduce a linear eigenfunction constraint for the D$\Delta$KP system and obtain a combined semi-discrete Burgers (sdBurgers) hierarchy. In the third one, we consider another linear eigenfunction constraint for the modified D$\Delta$KP system and obtain the same combined sdBurgers hierarchy. All these constraint results are proved by using recursive algebraic structures of the involved integrable hierarchies generated by their master symmetries.

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Jin Liu, Da-jun Zhang. 2026-03-09. Constraints of the D$\Delta$KP hierarchy to the semi-discrete AKNS and Burgers hierarchies. https://arxiv.org/abs/2603.08301

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