The Toda lattice is a prime example of a lattice system that is completely integrable, in the sense that it admits a Lax pair, https://doi.org/10.1143/PTP.51.703, making it easy to find soliton solutions.
Generalizing this example, I'm wondering if there is a lattice system that is both frustrated (in the sense there is an underlying graph structure whose edges cannot be simultaneously satisfied) but admits a completely integrable dynamics. For example, if I have a 2D Ising model with arbitrary bonds and linearly relaxed spins, is it possible to write down some ODE to govern the evolution of the spins such that the dynamics is integrable?
What are some of the standard techniques people use to find soliton solutions in these frustrated systems?
