Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs

• URL: http://arxiv.org/abs/2008.04897v2
• Date: Thu, 14 Jan 2021 16:35:24 GMT
• Title: Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
• Authors: Gamal Mograby, Maxim Derevyagin, Gerald V. Dunne, Alexander Teplyaev
• Abstract summary: We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. We 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.
• Score: 62.997667081978825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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