格拉斯曼的
数学
沃伦斯基
孤子
等级制度
简并能级
纯数学
代数曲线
有理函数
曲线的奇点
数学分析
代数数
三角晶系
非线性系统
量子力学
物理
经济
晶体结构
化学
市场经济
结晶学
出处
期刊:Nonlinearity
[IOP Publishing]
日期:2018-06-28
卷期号:31 (8): 3567-3590
被引量:10
标识
DOI:10.1088/1361-6544/aabf00
摘要
It is known that soliton solutions of the KP-hierarchy corresponds to singular rational curves with only ordinary double points. In this paper we study the degeneration of theta function solutions corresponding to certain trigonal curves. We show that, when the curves degenerate to singular rational curves with only ordinary triple points, the solutions tend to some intermediate solutions between solitons and rational solutions. They are considered as cerain limits of solitons. The Sato Grassmannian is extensively used here to study the degeneration of solutions, since it directly connects solutions of the KP-hierarchy to the defining equations of algebraic curves.We define a class of solutions in the Wronskian form which contains soliton solutions as a subclass and prove that, using the Sato Grassmannian, the degenerate trigonal solutions are connected to those solutions by certain gauge transformations
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