Evolution of the Topological Linear Defects

In the light of ø-mapping method and topological current theory, the topological structure and the topological quantization of topological linear defects are obtained under the condition that Jacobian J (ø / v ) ≠ 0. When J ( ø / v ) = 0, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the generation, annihilation and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of ø-mapping, respectively.