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Numerical Inverse Scattering for the Toda Lattice

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Deniz Bilman, Thomas Trogdon

Exactly Solvable and Integrable Systems · Submitted 7 Aug 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically.

how it is stated · asserted 1.00 read the record →

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arXiv ID1508.01788 (version 4)
Pith IDGYOVBZP7, Pith's permanent record of this paper and its review
CitationDeniz Bilman, Thomas Trogdon. "Numerical Inverse Scattering for the Toda Lattice." arXiv:1508.01788 (2015). https://pith.science/paper/GYOVBZP7
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,641 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.08 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in $\mathcal O(1)$ operations for arbitrary points in the $(n,t)$-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because $(n,t)$ appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. contribution 0.94 0.93 0.47 asserted 1.00
s1 Deformations for the RH problem are incorporated so that the IST can be evaluated in $\mathcal O(1)$ operations for arbitrary points in the $(n,t)$-domain, including short- and long-time regimes. method 0.76 0.87 0.27 asserted 1.00
s2 No time-stepping is required to compute the solution because $(n,t)$ appear as parameters in the associated RH problem. method 0.91 0.82 0.16 asserted 1.00
s3 The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously. result 0.46 0.89 0.18 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a method to compute the inverse scattering transform (IST) for the famed Toda lattice by solving the associated Riemann--Hilbert (RH) problem numerically. Deformations for the RH problem are incorporated so that the IST can be evaluated in $\mathcal O(1)$ operations for arbitrary points in the $(n,t)$-domain, including short- and long-time regimes. No time-stepping is required to compute the solution because $(n,t)$ appear as parameters in the associated RH problem. The solution of the Toda lattice is computed in long-time asymptotic regions where the asymptotics are not known rigorously.

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