Solitons, Instantons, and Twistors
By Maciej Dunajski. 2010
151 citations recorded by the source corpus.
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e5bc1d5cfe03352b9ee2a4300fa25e0850ca4363
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In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Pseudospectrum and Black Hole Quasinormal Mode Instability (2020, background): “[86]; see [85] for an alternative approach in terms of Darboux transformations).”