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On a Solitonic Specialisation for the General Solutions of Some Two-Dimensional Completely Integrable Systems
High Energy Physics - Theory · Submitted 21 Dec 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely integrable systems arising in the framework of the group-algebraic approach, including the \lq\lq non-abelian" version of the affine Toda theory.
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The abstract, sentence by sentence
Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely integrable systems arising in the framework of the group-algebraic approach, including the \lq\lq non-abelian" version of the affine Toda theory.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely integrable systems arising in the framework of the group-algebraic approach, including the \lq\lq non-abelian" version of the affine Toda theory. | contribution 0.99 | 0.85 | 0.47 | asserted 0.98 |
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The paper
Original abstract
Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely integrable systems arising in the framework of the group-algebraic approach, including the \lq\lq non-abelian" version of the affine Toda theory.
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How the literature uses it
5 arXiv papers cite this in 8 sentences
Papers citing it · 1 sentence without a confident label
Uses its method or tool 2 papers
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As explained in hnsolitonbd we construct the soliton solutions using the so-called solitonic specialization procedure [ref] .
The Bullough-Dodd model coupled to matter fields · Soliton solutions · 1.00
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The $n$-soliton solutions are obtained by taking the constant group element $h$ introduced in gaussdecomp as the product of $n$ exponentials of eigenvectors of the oscillators $b_2n+1$ [ref] , namely the vertex operators defined in vertexdef, i.e. h=∏_i=1^n e^a_i V\(z_i\). solitonh Therefore, using psivac and vertexeigen one gets that Ψ_vac h Ψ_vac^-1 = ∏_i=1^n e^a_i e^Γ\(z_i\) V\(z_i\)= ∏_i=1^n \(1+a_i e^Γ\(z_i\) V\(z_i\)\), nsolitontauoperator where we have used the nilpotency property vertexnipotent of the vertex operator and have introduced Γ\(z_i\)≡z_i x_+-x_-/z_i.
A simple formula for the conserved charges of soliton theories · Soliton solutions · 0.88
Cites it as background 2 papers
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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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There are also two additional approaches to the problem, being a development of the Leznov–Saveliev method [ref] , and of the Bäcklund–Darboux transformation [ref] .
Abelian Toda solitons revisited · Introduction · 0.89
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