Physics – Mathematical Physics
Scientific paper
2004-03-12
Nonlinearity 18 (2005) 543-557.
Physics
Mathematical Physics
15 pages, Abstract and introduction rewritten to clarify the objectives of the paper. This is the final version which will app
Scientific paper
10.1088/0951-7715/18/2/005
It is well known that twistor constructions can be used to analyse and to obtain solutions to a wide class of integrable systems. In this article we express the standard twistor constructions in terms of the concept of an admissible family of rational curves in certain twistor spaces. Examples of of such families can be obtained as subfamilies of a simple family of rational curves using standard operations of algebraic geometry. By examination of several examples, we give evidence that this construction is the basis of the construction of many of the most important solitonic and algebraic solutions to various integrable differential equations of mathematical physics. This is presented as evidence for a principal that, in some sense, all soliton-like solutions should be constructable in this way.
Dunajski Maciej
Gindikin Simon
Mason Lionel J.
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