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Poisson structures for difference equations

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Charalampos A. Evripidou, G. R. W. Quispel, John A. G. Roberts

Exactly Solvable and Integrable Systems · Submitted 19 Jun 2018

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

The authors' main claim We give examples of quadratic Poisson structures that arise for the Kadomtsev-Petviashvili (KP) type maps which follow from a travelling-wave reduction of the corresponding integrable partial difference equation.

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arXiv ID1806.07233 (version 2)
Pith IDWND7KVNX, Pith's permanent record of this paper and its review
CitationCharalampos A. Evripidou, G. R. W. Quispel, John A. G. Roberts. "Poisson structures for difference equations." arXiv:1806.07233 (2018). https://pith.science/paper/WND7KVNX
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,929 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. We also study the inverse problem, given a log-canonical Poisson structure to find a difference equation preserving this structure. We give examples of quadratic Poisson structures that arise for the Kadomtsev-Petviashvili (KP) type maps which follow from a travelling-wave reduction of the corresponding integrable partial difference equation.

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 study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. contribution 1.00 0.90 0.14 asserted 0.69
s1 We also study the inverse problem, given a log-canonical Poisson structure to find a difference equation preserving this structure. contribution 1.00 0.93 0.08 asserted 0.96
s2 We give examples of quadratic Poisson structures that arise for the Kadomtsev-Petviashvili (KP) type maps which follow from a travelling-wave reduction of the corresponding integrable partial difference equation. result 0.85 0.85 0.15 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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 study the existence of log-canonical Poisson structures that are preserved by difference equations of special form. We also study the inverse problem, given a log-canonical Poisson structure to find a difference equation preserving this structure. We give examples of quadratic Poisson structures that arise for the Kadomtsev-Petviashvili (KP) type maps which follow from a travelling-wave reduction of the corresponding integrable partial difference equation.

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