Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
arXiv:2008.04897 · doi:10.1063/5.0025475
Abstract
We consider discrete one dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons {for static potentials} on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z-graded graph.
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