Algebraic geometry and stability for integrable systems

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5 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)74-82
Number of pages9
JournalPhysica D: Nonlinear Phenomena
StatePublished - Jan 15 2015


  • Algebraic curves
  • Algebraic geometry
  • Integrable systems
  • Lax representation
  • Stability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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