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Pregled bibliografske jedinice broj: 347525

On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equation


Saša Krešić-Jurić
On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equation // Journal of Mathematical Physics, 47 (2006), 6; 063501-1 (međunarodna recenzija, članak, znanstveni)


Naslov
On the Birkhoff factorization problem for the Heisenberg magnet and nonlinear Schroedinger equation

Autori
Saša Krešić-Jurić

Izvornik
Journal of Mathematical Physics (0022-2488) 47 (2006), 6; 063501-1

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

Ključne riječi
Birkhoff factorization; Heisenberg magnet; Segal-Wilson Grassmannian

Sažetak
A geometrical description of the Heisenberg magnet (HM) equation with classical spins is given in terms of flows on the quotient space $G/H_+$ where $G$ is an infinite dimensional Lie group and $H_+$ is a subgroup of $G$. It is shown that the HM flows are induced by an action of $\R^2$ on $G/H_+$, and that the HM equation can be integrated by solving a Birkhoff factorization problem for $G$. For the HM flows which are Laurent polynomials in the spectral variable we derive an algebraic transformation between solutions of the nonlinear Schr\"{; ; ; o}; ; ; dinger (NLS) and Heisenberg magnet equation. The Birkhoff factorization problem for $G$ is treated in terms of the geoemetry of the Segal-Wilson Grassmannian $Gr(H)$. The solution of the problem is given in terms of a pair of Baker functions for special subspaces in $Gr(H)$. The Baker functions are constructed explicitly for subspaces which yield multisoliton solutions of NLS and HM equations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
177-0372794-2816 - Lieve grupe, integrabilni sistemi i simetrije (Saša Krešić-Jurić, )

Ustanove
Prirodoslovno-matematički fakultet, Split

Autor s matičnim brojem:
Slavko Saša, (94260)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus