Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two
نویسنده
چکیده
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. 2000 MSC: 35Q53, 53A04, 14H45, 11J89 PACS: 02.30.-f, 05.20.-y, 46.70.Hg, 05.45.Yv key words: hyperelliptic function, sigma function, space curve, elastica
منابع مشابه
Hyperelliptic loop solitons with genus g: investigations of a quantized elastica
In the previous work (J. Geom. Phys. 39 (2001) 50-61), the closed loop solitons in a plane, 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 ...
متن کاملSupersymmetric Q Solitons of Arbitrary Genus
We construct “Flying Saucer” solitons in supersymmetric N = 2 gauge theory which is known to support BPS domain walls with a U(1) gauge field localized on its worldvolume. We demonstrate that this model supports exotic particle-like solitons whose topology is largely arbitrary: closed orientable surfaces in three-dimensional space which can have arbitrary genus. In particular, we focus on Q tor...
متن کاملDevelopment of closed-loop supply chain mathematical model (cost-benefit-environmental effects) under uncertainty conditions by approach of genetic algorithm
In the current world, the debate on the reinstatement and reuse of consumer prod-ucts has become particularly important. Since the supply chain of the closed loop is not only a forward flow but also a reverse one; therefore, companies creating integ-rity between direct and reverse supply chain are successful. The purpose of this study is to develop a new mathematical model for closed loop suppl...
متن کاملMathematical Formulation and Solving of Green Closed-loop Supply Chain Planning Problem with Production, Distribution and Transportation Reliability
In this paper, developed a new multi-product, multi-period, and multi-level closed-loop green supply chain planning model under uncertain conditions. The formulated model consists of five objective functions, which minimize the cost of the supply chain, minimize the CO2 emission of transportation vehicles, maximize the reliability of manufacturing and distribution centers, maximize t...
متن کاملImpact of government’s policies on competition of two closed-loop and regular supply chains
With progressing technologies and new features of production, new products compete with older ones in markets. Indeed, new products initiate contest with olden ones and this process repeats in different productions lifetime several times. In this situation recycling the olden products seems to be significant for supply chains. Governments often levy special tariffs for these products as a contr...
متن کامل