The topological quantization and bifurcation of the topological linear defects

Duan, Yishi; Jiang, Ying; Yang, Guohong

The topological quantization and bifurcation of the topological linear defects

Authors

Duan, Yishi

Jiang, Ying

Yang, Guohong

Description

In the light of $ϕ$-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that the Jacobian $J(ϕ/v) \neq 0$. When $J(ϕ/v) = 0$, it is shown that there exist the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of $ϕ$-mapping, respectively.
10 pages, no figures, LATEX file