Tyurin parameters and elliptic analogue of nonlinear Schrödinger hierarchy
| dc.creator | Takasaki, Kanehisa | |
| dc.date | 2003-07-18 | |
| dc.date | 2004-04-27 | |
| dc.date.accessioned | 2026-07-07T05:34:52Z | |
| dc.date.available | 2026-07-07T05:34:52Z | |
| dc.description | Two "elliptic analogues'' of the nonlinear Schrödinger hiererchy are constructed, and their status in the Grassmannian perspective of soliton equations is elucidated. In addition to the usual fields $u,v$, these elliptic analogues have new dynamical variables called ``Tyurin parameters,'' which are connected with a family of vector bundles over the elliptic curve in consideration. The zero-curvature equations of these systems are formulated by a sequence of $2 \times 2$ matrices $A_n(z)$, $n = 1,2,...$, of elliptic functions. In addition to a fixed pole at $z = 0$, these matrices have several extra poles. Tyurin parameters consist of the coordinates of those poles and some additional parameters that describe the structure of $A_n(z)$'s. Two distinct solutions of the auxiliary linear equations are constructed, and shown to form a Riemann-Hilbert pair with degeneration points. The Riemann-Hilbert pair is used to define a mapping to an infinite dimensional Grassmann variety. The elliptic analogues of the nonlinear Schrödinger hierarchy are thereby mapped to a simple dynamical system on a special subset of the Grassmann variety. | |
| dc.description | latex2e, 36 pp, no figure; (v2) minor changes, mostly typos; (v3) Title changed, text fully revised with new results; (v4) serious errors in section 5 corrected; (v5) proof of main results is improved; (v6) minor change in proof of Lemma 10 etc; (v7) final version for publication; (v8) typos corrected. Journal of Mathematical Sciences, University of Tokyo (to appear) | |
| dc.identifier | https://arxiv.org/abs/nlin/0307030 | |
| dc.identifier | http://arxiv.org/abs/nlin/0307030 | |
| dc.identifier | J. Math. Sci. Univ. Tokyo 11 (2004), 91-131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80532 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Quantum Algebra | |
| dc.title | Tyurin parameters and elliptic analogue of nonlinear Schrödinger hierarchy | |
| dc.type | text |