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Microscopic conservation laws for integrable lattice models

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Abstract

We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz–Ladik system. The principal thrust of the paper is the development of microscopic conservation laws that witness the conservation of the perturbation determinant under these dynamics. In this way, we obtain discrete analogues of objects that we found essential in our recent analyses of KdV, NLS, and mKdV. In concert with this, we revisit the classical topic of microscopic conservation laws attendant to the (renormalized) trace of the Green’s function.

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Acknowledgements

R. K. was supported by NSF Grant DMS-1856755 and M. V. by NSF Grant DMS-1763074.

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  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095, USA

    Benjamin Harrop-Griffiths, Rowan Killip & Monica Vişan

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  1. Benjamin Harrop-Griffiths
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  2. Rowan Killip
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  3. Monica Vişan
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Correspondence to Benjamin Harrop-Griffiths.

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Communicated by Adrian Constantin.

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Harrop-Griffiths, B., Killip, R. & Vişan, M. Microscopic conservation laws for integrable lattice models. Monatsh Math 196, 477–504 (2021). https://doi.org/10.1007/s00605-021-01529-5

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