Relations in a Loop Soliton as a Quantized Elastica

Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two

Closed loop solitons in a plane, whose curvatures obey the modified Korteweg-de Vries equation, were investigated. It was shown that their tangential vectors are expressed by ratio of Weierstrass sigma functions for genus one case and ratio of Baker's sigma functions for the genus two case. This study is closely related to classical and quantized elastica problems.

Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica

In the previous work (J. Geom. Phys. {\bf{39}} (2001) 50-61), the closed loop solitons in a plane, \it i.e., loops whose curvatures obey the modified Korteweg-de Vries equations, were investigated for the case related to algebraic curves with genera one and two. This article is a generalization of the previous article to those of hyperelliptic curves with general genera. It was proved that the tangential angle of loop soliton is expressed by the Weierstrass hyperelliptic al function for a given hyperelliptic curve $y^2 = f(x)$ with genus $g$.

Quantized representation of some nonlinear integrable evolution equations on the soliton sector

The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple quantized representation of these equations and their soliton solutions over a Fock space of bosons or of fermions. The classical nonlinear wave equation becomes a nonlinear equation for an operator. The solution of this equation is constructed through the operator analog of the Hirota transformation. The classical N-solitons solution is the expectation value of the solution operator in an N-particle state in the Fock space.

二维多频孤子的量子化输运

Quantized transport of two-dimensional multifrequency solitons

本文研究二维二次孤子在周期性χ^(2)材料中的Thouless泵浦，发现大振幅孤子可实现稳定量子化输运，且输运方向由纵向周期之比的无理数极限决定。