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Reality conditions of loop solitons genus \(g\): hyperelliptic am functions. (English) Zbl 1134.37034
Summary: This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic curve. We also compute winding numbers of loop solitons.
MSC:
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35Q53 KdV equations (Korteweg-de Vries equations)
14H45 Special algebraic curves and curves of low genus
14H70 Relationships between algebraic curves and integrable systems
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