Abstract

The scattering of magnetic flux tubes in superconductors is studied First, we introduce the Abehan-Higgs model, which describes vortices in a superconductor, and the Euler-Lagrange equations which minimize the energy density given by this model Static vortex solutions satisfying these equations are reviewed. A technique proposed by on Manton [1] in which slowly changing solutions are approximated by a special family of time-independent solutions is described. Time-dependent solutions over small intervals are also studied Then the existence and the symmetries of the time-dependent solutions are studied. This analysis rules out all cases other than 0°, 90° or 180° scattenng of two vortices The proof of the Cauchy-Kowalewskyi theorem for a system of first order quasi-linear partial differential equations of (n+1) independent variables and m unknown functions is given. The Taylor expansion of the initial data near the origin is studied. The Cauchy Kowalewskyi theorem is applied to find the solutions of the time-dependent Euler-Lagrange equations near the origin. This study proves that our solution describes 90° scattenng Mathematica programs to calculate the senes solutions are also supplied.