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Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations

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Arthemy V. Kiselev, Thomas Wolf

Mathematical Physics · Submitted 24 Nov 2005

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

The authors' main claim We construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0511071 (version 3)
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CitationArthemy V. Kiselev, Thomas Wolf. "Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations." arXiv:math-ph/0511071 (2005). https://pith.science/paper/RDHYSG7H
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,959 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters.

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 construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. contribution 1.00 0.97 0.64 asserted 1.00
s1 Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. result 0.92 0.86 0.15 asserted 1.00
s2 Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. method 0.98 0.87 0.06 asserted 0.99
s3 A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. result 0.84 0.75 0.08 asserted 1.00
s4 A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. result 0.63 0.95 0.09 asserted 1.00
s5 Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters. contribution 0.80 0.96 0.19 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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  • references and citing sentences
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  • 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 construct new integrable coupled systems of N=1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters.

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