On the Integrable Lattices of Octahedron Type

Xiaoxue Xu, Visiting Research Fellow from Zhengzhou University at the University of Leeds

The discrete integrable system is an important part in the theory of soliton. A classification of 2-dimensional discrete integrable systems is given in the ABS hierarchy, which satisfy the consistency-around-the-cube (CAC) property. In the 3-dimensional situation, five integrable lattices were discovered basing on the consistency around the octahedron.

In this talk, I will discuss the finite genus solutions of the (Semi-)discretized pKP and pMKP equations with the help of the nonlinearization technique. In particular, we have made a surprising observation about the continuum limit of the lattice Schwarzian KP equation.

Joint work with Cewen Cao and Da-jun Zhang.

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Be Curious 2020