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Hirota's Solitons in the Affine and the Conformal Affine Toda Models

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H.Aratyn, C.P. Constantinidis, L.A. Ferreira, J.F. Gomes, A.H. Zimerman

High Energy Physics - Theory · Submitted 14 Dec 1992

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

The authors' main claim We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/9212086 (version 1)
Pith IDDNX56SCK, Pith's permanent record of this paper and its review
CitationA.H. Zimerman, C.P. Constantinidis, H.Aratyn, J.F. Gomes, L.A. Ferreira. "Hirota's Solitons in the Affine and the Conformal Affine Toda Models." arXiv:hep-th/9212086 (1992). https://pith.science/paper/DNX56SCK
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,587 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.

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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 use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. method 0.54 0.96 0.31 asserted 1.00
s1 Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. result 0.65 0.94 0.19 asserted 1.00
s2 We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. result 0.88 0.96 0.28 asserted 1.00
s3 Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis. method 0.58 0.30 0.09 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

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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

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Original abstract

We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two different type of degeneracies encountered in the Hirota's perturbation approach. We also derive an universal mass formula for all Hirota's solutions to the Affine Toda model valid for all underlying Lie groups. Embedding of the Affine Toda model in the Conformal Affine Toda model plays a crucial role in this analysis.

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6 arXiv papers cite this in 9 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Papers citing it · 7 sentences without a confident label

Uses its method or tool 1 paper
  • Following the Hirota's approach [ref] , one introduces $τ$-functions connected with $Γ_α$ by the relation [equation] where we assume that the $τ$-functions are defined for all integer values of the index $α$.

    Abelian Toda solitons revisited · Hirota's method · 0.98

Cites it as background 1 paper
  • The most known and elaborated among them are the Hirota's method [ref] , successfully applied to many particular cases of Abelian affine Toda systems [ref] ; the vertex operators approach of [ref] based on a proper specialisation of the Leznov–Saveliev method [ref] , see also [ref] for more details and the relation to the dressing symmetry; and the formalism of rational dressing developed by Mikhailov [ref] on the basis of a general dressing procedure proposed by Zakharov and Shabat [ref] .

    More non-Abelian loop Toda solitons · Introduction · 0.86

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