A note on an integrable discretization of the nonlinear Schrödinger equation

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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.

Original languageEnglish
Pages (from-to)1121-1136
Number of pages16
JournalInverse Problems
Volume13
Issue number4
DOIs
StatePublished - 1997
Externally publishedYes

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