| 韩众,陈勇,郎艳怀.(2+1)-维破裂孤子方程的群叶状 方法和显式解[J].数学年刊A辑,2018,(4):377~390 |
| (2+1)-维破裂孤子方程的群叶状 方法和显式解 |
| Group Foliation and Explicit Solutions of the (2+1)-Dimensional Breaking Soliton Equation |
| Received:December 06, 2016 Revised:December 05, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0003 |
| 中文关键词: Group foliation, Equivariant moving frames, Differential invariants, $(2+1)$-Dimensional breaking soliton equation |
| 英文关键词:Group foliation, Equivariant moving frames, Differential invariants, $(2+1)$-Dimensional breaking soliton equation |
| 基金项目:本文受到全球变化研究项目(No.2015CB953904),国家自然科学基金(No.11675054,No.11275072)
和上海物联网可信软件协作创新中心(No.ZF1213)的资助. |
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| 中文摘要: |
| 利用等变活动标架理论, 研究$(2+1)${-}维破裂孤子方程的群叶状方法和显式解.
原方程的对称群的无穷维部分被用来产生整个解空间的叶状结构,
于是分解系统就继承了对称群的有限维部分. 求解的过程完全符号化和算法化.
利用群叶状方法, 破裂孤子方程的一些显式精确解被得到,
这些解关于无穷维对称子群封闭. |
| 英文摘要: |
| Group foliation of the (2+1)-dimensional breaking soliton equation is performed within the theory of equivariant moving frames. The infinite-dimensional part of the admitted symmetry group is utilized to produce a foliation of its entire solution space, so the resolving system inherits only the finite-dimensional part of the symmetry group. The procedure of the method is completely symbolic and algorithmic. With the group foliation reduction method, some solutions of the breaking soliton equation are obtained in an explicit form which are closed with respect to the regarding infinite-dimensional subgroup. |
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