Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphs

Mograby, Gamal; Derevyagin, Maxim; Dunne, Gerald V.; Teplyaev, Alexander

doi:10.1063/5.0025475

Title: Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted $Z$ -graded graphs

Journal Article · Tue Apr 20 00:00:00 EDT 2021 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/5.0025475· OSTI ID:1851356

Mograby, Gamal ^[1]; Derevyagin, Maxim ^[1];

^[1];

^[1]

Univ. of Connecticut, Storrs, CT (United States)

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to $Z$ -graded graphs. We identify conditions that 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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Research Organization:: Univ. of Connecticut, Storrs, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: SC0010339; 1613025; 2008844

OSTI ID:: 1851356

Alternate ID(s):: OSTI ID: 1778582

Journal Information:: Journal of Mathematical Physics, Vol. 62, Issue 4; ISSN 0022-2488

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

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Title: Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted $Z$ -graded graphs