RECORD
On Soliton Content of Self Dual Yang-Mills Equations
High Energy Physics - Theory · Submitted 19 Nov 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method.
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.
Open the compiled record
The abstract, sentence by sentence
Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map $ \C^4 \to \C^{\infty } $ satisfying a simple system of linear equations formulated below one can pull back the (generalized) Drinfeld-Sokolov hierarchies to the Self Dual Yang-Mills equations. This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method. In particular this class contains the solutions obtained via the symmetry reductions of the Self Dual Yang-Mills equations. It also contains genuine 4 dimensional solutions . The method can be used to study the symmetry reductions and as an example of that we get an equation exibiting breaking solitons, formulated by O. Bogoyavlenskii, as one of the $2 + 1 $ dimensional reductions of the Self Dual Yang-Mills equations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. | contribution 0.96 | 0.92 | 0.31 | asserted 1.00 |
| s1 | We show that for each map $ \C^4 \to \C^{\infty } $ satisfying a simple system of linear equations formulated below one can pull back the (generalized) Drinfeld-Sokolov hierarchies to the Self Dual Yang-Mills equations. | result 0.81 | 0.91 | 0.44 | asserted 1.00 |
| s2 | This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method. | interpretation 0.95 | 0.76 | 0.38 | hedged possibility 0.99 |
| s3 | In particular this class contains the solutions obtained via the symmetry reductions of the Self Dual Yang-Mills equations. | result 0.91 | 0.71 | 0.10 | asserted 1.00 |
| s4 | It also contains genuine 4 dimensional solutions . | result 0.95 | 0.78 | 0.11 | asserted 1.00 |
| s5 | The method can be used to study the symmetry reductions and as an example of that we get an equation exibiting breaking solitons, formulated by O. | contribution 0.57 | 0.82 | 0.07 | asserted 0.71 |
| s6 | Bogoyavlenskii, as one of the $2 + 1 $ dimensional reductions of the Self Dual Yang-Mills equations. | result 0.73 | 0.56 | 0.05 | asserted 0.93 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map $ \C^4 \to \C^{\infty } $ satisfying a simple system of linear equations formulated below one can pull back the (generalized) Drinfeld-Sokolov hierarchies to the Self Dual Yang-Mills equations. This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method. In particular this class contains the solutions obtained via the symmetry reductions of the Self Dual Yang-Mills equations. It also contains genuine 4 dimensional solutions . The method can be used to study the symmetry reductions and as an example of that we get an equation exibiting breaking solitons, formulated by O. Bogoyavlenskii, as one of the $2 + 1 $ dimensional reductions of the Self Dual Yang-Mills equations.
Human review
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.