Nahm’s equations, singular point analysis, and integrability. (English) Zbl 0621.34008
A singular point analysis (Painlevé test) for certain special cases of Nahm’s equations is performed. It is shown that there are cases in which the equations do not pass the test. The Laurent expansion does not contain the right number of arbitrary expansion coefficients. Nevertheless the systems under consideration are completely integrable.
MSC:
| 34A99 | General theory for ordinary differential equations |
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
| 34A05 | Explicit solutions, first integrals of ordinary differential equations |
Keywords:
completely integrable system; monopole solutions in Yang-Mills theory; singular point analysis; Painlevé test; Nahm’s equations; Laurent expansion; expansion coefficientsReferences:
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