Integrable and solvable systems, and relations among them
1985 ◽
Vol 315
(1533)
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pp. 451-457
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Keyword(s):
The Self
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There are several different classes of differential equations that may be described as ‘integrable’ or ‘solvable’. For example, there are completely integrable dynamical systems; equations such as the sine—Gordon equation, which admit soliton solutions; and the self-dual gauge-field equations in four dimensions (with generalizations in arbitrarily large dimension). This lecture discusses two ideas that link all of these together: one is the Painlevé property, which says (roughly speaking) that all solutions to the equations are meromorphic; the other is that many of the equations are special cases (i.e. reductions) of others.
1978 ◽
Vol 362
(1711)
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pp. 572-572
2003 ◽
Vol 321
(3-4)
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pp. 467-481
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2002 ◽
Vol 71
(8)
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pp. 2071-2071
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1994 ◽
Vol 28
(5)
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pp. 305-310
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1994 ◽
Vol 06
(06)
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pp. 1301-1338
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2009 ◽
Vol 23
(04)
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pp. 607-621
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Keyword(s):