标题： 正则条件到sine-Gordon方程和有限相空间中的准周期解 显示英文标题

标题： Reality conditions to the sine-Gordon equation and quasi-periodic solutions in finite phase spaces

摘要： 拟周期解用$\wp_{1,2g-1}$函数表示，现实条件被完全指定。 这一新结果导致了非线性波解的计算和图形表示。 详细介绍了通过代数几何积分方法获得有限间隙解的方法，以及在环代数$\mathfrak{su}(2)$的伴随轨道上构造 sine-Gordon 层次结构的方法。 显示英文摘要

摘要： Quasi-periodic solutions to the sine-Gordon equation are expressed in terms of $\wp_{1,2g-1}$-function, and reality conditions are completely specified. This new result leads to computation and graphical representation of non-linear wave solutions. A way of obtaining the finite-gap solutions by means of algebro-geometric integration is exposed in detail, as well as the construction of the sine-Gordon hierarchy on coadjoint orbits in the loop algebra of $\mathfrak{su}(2)$.