标题： 孤子晶格的高阶相互作用的近可积性 显示英文标题

标题： Near integrability of kink lattice with higher order interactions

摘要： 在论文中，我们利用Manton的分析方法来研究在$1+1$维场论中，孤子和反孤子之间大距离时的力。 相关的势能具有无限阶的指数形式修正，每一阶的系数都被确定。 这些系数也可以通过求解真空周围的涨落方程得到。 在最低阶近似下，孤子晶格代表Toda晶格。 随着更高阶修正项的引入，孤子晶格可以代表一种一般的Toda晶格。 当只有两个格点时，孤子晶格是经典可积的。 如果晶格的格点数大于二，孤子晶格是不可积的，但是一个接近可积的系统。 我们利用Flaschka变量来研究孤子晶格的Lax对。 这些Flaschka变量具有有趣的代数关系，非可积性可以被体现出来。 我们还讨论了变形的开Toda晶格的高阶哈密顿量，其结果与普通变形的Toda晶格类似。 显示英文摘要

摘要： In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential pattern, and coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuation around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of the generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but a near integrable system. We take use of the Flaschka's variables to study the Lax pair of the kink lattice. These Flaschka's variables have interesting algebraic relations and the non-integrability can be manifested. We also discussed the higher Hamiltonians for the deformed open Toda lattice, which has a similar result as the ordinary deformed Toda.