dorsal/arxiv
View SchemaA note on the integrable discretization of the nonlinear Schr\"odinger equation
| Authors | Yuri B. Suris |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9701010 |
| URL | https://arxiv.org/abs/solv-int/9701010 |
| DOI | 10.1088/0266-5611/13/4/016 |
| Journal | Inverse Problems, 1997, V. 13, p. 1121-1136. |
Abstract
We revisit integrable discretizations for the nonlinear Schr\"odinger 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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"abstract": "We revisit integrable discretizations for the nonlinear Schr\\\"odinger\nequation due to Ablowitz and Ladik. We demonstrate how their main drawback, the\nnon-locality, can be overcome. Namely, we factorize the non-local difference\nscheme into the product of local ones. This must improve the performance of the\nscheme in the numerical computations dramatically. Using the equivalence of the\nAblowitz--Ladik and the relativistic Toda hierarchies, we find the\ninterpolating Hamiltonians for the local schemes and show how to solve them in\nterms of matrix factorizations.",
"arxiv_id": "solv-int/9701010",
"authors": [
"Yuri B. Suris"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0266-5611/13/4/016",
"journal_ref": "Inverse Problems, 1997, V. 13, p. 1121-1136.",
"title": "A note on the integrable discretization of the nonlinear Schr\\\"odinger equation",
"url": "https://arxiv.org/abs/solv-int/9701010"
},
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