In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing te...In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.展开更多
The adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equa...The adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex （2＋2）-dimensional version of the （2＋ 1）-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in （2＋l）-dimensional case.展开更多
We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show ...We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.展开更多
基金This work is partially supported by the National Natural Science Foundation of China (Grant Nos.10071067,10471119)the Excellent Yong Teachers Program of the Ministry of Education of China.
文摘In this paper, we study the asymptotic behavior of solutions of the Ginzburg-Landau equation with impurity. We prove that, asymptotically, the vortex-lines evolve according to the mean curvature flow with a forcing term in the sense of the weak formulation.
基金supported by Russian Foundation of Basic Research(Grants Nos.16-01-00117 and 16-52-12012)the Program of support of Leading Scientific Schools(Grants No.NSh-9110.2016.1)the Program of Presidium of Russian Academy of Sciences“Nonlinear dynamics”
文摘The adiabatic limit procedure associates with every solution of Abelian Higgs model in （2 ^- 1） dimensions a geodesic in the moduli space of static solutions. We show that the same procedure for Seiberg- Witten equations on 4-dimensional symplectic manifolds introduced by Taubes may be considered as a complex （2＋2）-dimensional version of the （2＋ 1）-dimensional picture. More precisely, the adiabatic limit procedure in the 4-dimensional case associates with a solution of Seiberg-Witten equations a pseudoholomorphic divisor which may be treated as a complex version of a geodesic in （2＋l）-dimensional case.
文摘We consider the (2+1)-dimensional Abelian Higgs model, governed by the Ginzburg-Landau action functional and describe the adiabatic limit construction for this model. Then we switch to the 4-dimensional case and Show that the Taubes correspondence may be considered as a (2+2)-dimensional analogue of the adiabatic limit construction.
