Naslov
The Heisenberg magnet equation and the Birkhoff factorization

Autori
Saša Krešić-Jurić

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (0430-3202) 53 (2007); 299-308

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Birkhoff factorization; Heisenberg magnet; solitons

Sažetak
A geometrical description of the Heisenberg magnet (HM)with classical spins is given in terms of flows on the homogeneous space $G/H_+$ where $G$ is a Banach-Lie group and $G_+$ is a subgroup of $G$. The flows are induced by an action of the abelian group $R^2$ on $G/H_+$, and the solutions of the HM equation can be found by solving a Birkhoff factorization problem for $G$. The gauge transformation between the HM and nonlinear Schroedinger (NLS) equations is interpreted as a transformation between a canonical pair of Birkhoff factorizations for $G$. It is shown that for the HM flows which are Laurent polynomials in the spectral variable this transformation gives rise to a map between the HM and NLS solutions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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