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A note on the integrable discretization of the nonlinear Schrödinger equation

Yuri B. Suris
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Abstract

We revisit integrable discretizations for the nonlinear Schrödinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize the non-local difference scheme into the product of local ones. This must improve the performance of the scheme in the numerical computations dramatically. Using the equivalence of the Ablowitz--Ladik and the relativistic Toda hierarchies, we find the interpolating Hamiltonians for the local schemes and show how to solve them in terms of matrix factorizations.

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Yuri B. Suris. 1997-01-21. A note on the integrable discretization of the nonlinear Schrödinger equation. https://doi.org/10.1088/0266-5611%2F13%2F4%2F016

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