On symmetric primitive potentials

Dmitry Zakharov; Patrik Nabelek; Vladimir Zakharov

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On symmetric primitive potentials

Patrik Nabelek, Dmitry Zakharov, Vladimir Zakharov

Exactly Solvable and Integrable Systems · Submitted 26 Dec 2018

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

The authors' main claim We show that in this case, the resulting potential is symmetric, and describe how to analytically compute the potential as a power series.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,798 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite interval, called the dressing functions, which are not uniquely determined by the potential. The potential is constructed by solving a contour problem on the complex plane. In this paper, we consider a reduction where the dressing functions are equal. We show that in this case, the resulting potential is symmetric, and describe how to analytically compute the potential as a power series. In addition, we establish that if the dressing functions are both equal to one, then the resulting primitive potential is the elliptic one-gap potential.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4].	background 1.00	0.03	0.02	asserted 1.00
s1	Such a potential is determined by a pair of positive functions on a finite interval, called the dressing functions, which are not uniquely determined by the potential.	background 1.00	0.09	0.03	asserted 1.00
s2	The potential is constructed by solving a contour problem on the complex plane.	background 0.64	0.13	0.03	asserted 1.00
s3	In this paper, we consider a reduction where the dressing functions are equal.	contribution 0.91	0.61	0.06	asserted 0.85
s4	We show that in this case, the resulting potential is symmetric, and describe how to analytically compute the potential as a power series.	result 0.58	0.96	0.62	asserted 1.00
s5	In addition, we establish that if the dressing functions are both equal to one, then the resulting primitive potential is the elliptic one-gap potential.	result 0.99	0.94	0.21	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

The paper

Original abstract

The concept of a primitive potential for the Schroedinger operator on the line was introduced in [2,3,4]. Such a potential is determined by a pair of positive functions on a finite interval, called the dressing functions, which are not uniquely determined by the potential. The potential is constructed by solving a contour problem on the complex plane. In this paper, we consider a reduction where the dressing functions are equal. We show that in this case, the resulting potential is symmetric, and describe how to analytically compute the potential as a power series. In addition, we establish that if the dressing functions are both equal to one, then the resulting primitive potential is the elliptic one-gap potential.

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1 arXiv paper cite this in 9 sentences

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Papers citing it · 6 sentences without a confident label

Contests it 1 paper

Property (3) of the above nonlocal scalar Riemann–Hilbert problem did not appear in the papers [ref] , and this oversight was addressed in [ref] .

Algebro-Geometric Finite Gap Solutions to the Korteweg--de Vries Equation as Primitive Solutions · From the Baker–Akheizer Function to the Primitive Potential · contest 0.71

Cites it as background 1 paper

In previous papers on primitive solutions to the KdV equation, $R_1$ and $R_2$ were assumed to be nonnegative Hölder continuous functions on $[k_1,k_2]$ [ref] .

Algebro-Geometric Finite Gap Solutions to the Korteweg--de Vries Equation as Primitive Solutions · Finite Gap Solutions as Primitive Potentials · 0.81

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