Algebraic geometry and stability for integrable systems

PHYSICA D-NONLINEAR PHENOMENA

卷:291

Article

Izosimov, Anton^1,2 

[1] Univ Toronto, Toronto, ON M5S 1A1, Canada

[2] Moscow MV Lomonosov State Univ, Moscow, Russia

关键词: Integrable systems;    Lax representation;    Stability;    Algebraic geometry;    Algebraic curves;   

DOI  :  10.1016/j.physd.2014.10.006

来源: Elsevier

【 摘 要 】

In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with spectral parameter, the algebro-geometric method 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. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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