CHEN Zhihui,JIN Guanghui.Study on the existence of static solutions to the self - dual equation for the Chern - Simons Landau - Lifshitz model[J].Journal of Yanbian University,2022,(01):6-12.
Chern - Simons Landau - Lifshitz模型自对偶方程静态解的存在性
- Title:
- Study on the existence of static solutions to the self - dual equation for the Chern - Simons Landau - Lifshitz model
- 文章编号:
- 1004-4353(2022)01-0006-07
- 分类号:
- O175.22
- 文献标志码:
- A
- 摘要:
- 研究了Chern - Simons Landau - Lifshitz模型自对偶方程静态解的存在性问题.首先,利用数学分析理论和分离变量法得到了自对偶方程的静态解.其次,证明了当向量场满足A0=φ</sub>3-τ时自对偶方程的静态解满足Chern - Simons Landau - Lifshitz方程.最后,利用共变导数和向量运算法则证明了Chern - Simons Landau - Lifshitz模型具有能量守恒和规范不变的性质.
- Abstract:
- This paper considered the existence of static solutions to the self - dual case of the Chern - Simons Landau - Lifshitz model.First, the static solutions of the self - dual equations are obtained using the mathematical analysis technique and the separation variable method. Secondly, it is shown that the static solution of the self - dual equation also satisfies the Chern - Simons Landau - Lifshitz equation when the vector field is satisfied A0=φ</sub>3-τ.Finally, we use the covariant derivative and the vector operation rules to show that the Chern -Simons Landau - Lifshitz model has both energy - conservation and gauge - invariant properties.
参考文献/References:
[1] GUO B L, HAN Y Q.Global regular solutions for Landau - Lifshitz equation[J].Frontiers of Mathematics in China, 2006,1(4):538 - 568.
[2] 周艳婷.关于Landau - Lifshitz方程的一些研究[D].云南:云南师范大学,2018.
[3] 曹文慧,夏子伦,龙群飞.Landau - Lifshitz 方程解的基本性质[J].云南民族大学学报(自然科学版),2013,22(S1):80 - 81.
[4] YOU S J, GUO B L.Global well - posedness for high - order Landau - Lifshitz equation[J].Journal of Geometry and Physics, 2021,160:103966.
[5] 钟澎洪,陈兴发.Landau - Lifshitz方程平面波解的全局光滑性[J].数学物理学报,2021,41(3):729 - 739.
[6] CHANG N H, SHATAH J, UHLENBECK K.Schrödinger maps[J].Communications on Pure and Applied Mathematics, 2000,53(5):590 - 602.
[7] WEI J C, YANG J.Traveling vortex helices for Schrödinger map equations[J].Transactions of the American Mathematical Society, 2016,368(4):2599 - 2622.
[8] HUH H J.Blow - up solutions of modified Schrödinger maps[J].Communications in Partial Differential Equations, 2008,33(2):235 - 243.
[9] LIN F, WEI J.Travelling wave solutions of Schrödinger map equation[J].Comm Pure Appl Math, 2010,63(12):1585 - 1621.
[10] ALEXANDRU D I, CARLOS E K.Low - Regularity Schrödinger maps[J].Differential and Integral Equations, 2006,19(11):1271 - 1300.
备注/Memo
收稿日期: 2021-12-04
基金项目: 吉林省教育厅科学技术研究项目(JJKH20210564KJ)
第一作者: 陈智慧(1997—),女,硕士研究生,研究方向为偏微分方程.
通信作者: 金广辉(1987—),男,博士,讲师,研究方向为偏微分方程.