Algebraic geometry and stability for integrable systems
نویسنده
چکیده
In 1970s, a methodwas developed for integration of nonlinear equations bymeans of algebraic geometry. Starting froma Lax representationwith spectral parameter, the algebro-geometricmethod allows to solve the system explicitly in terms of theta functions of Riemann surfaces. However, the explicit formulas obtained in this way fail to answer qualitative questions such as whether a given singular solution is stable or not. In the present paper, the problem of stability for equilibrium points is considered, and it is shown that this problem can also be approached by means of algebraic geometry. © 2014 Elsevier B.V. All rights reserved.
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