THE FORMULA OF DALEMBERTS TYPE AND TIME PERIODICITY FOR THE MOTION OF RELATIVISTIC STRINGS IN THE MI

• 作 者: De-Xing Kong
• 机 构: DepartmentofMathematics,ShanghaiJiaoTongUniversity,Shanghai,200030,China
• 出 处: 2006 International Conference on Analysis and Applications(I
• 发表日期: 2006年6期

　　In this talk, we provide a formula of general solution of the equations for the motion of relativistic strings in the Minkowski space (IR)1+n, which is a little similar to the dAlemberts formula for linear wave equations.This gives a surprising fact: this kind of equations containing n nonlinear PDEs of second order possesses a solution formula of dAlemberts type.By introducing a new concept, named as generalized time-periodic function, we prove that, if the initial data is periodic, then the smooth solution of the Cauchy problem for this kind of equations is generalized time-periodic.This shows that the space-periodicity also implies the time-periodicity for the classical solution of the Cauchy problem for this kind of equations.This fact yields an interesting physical phenomenon: the motion of closed strings possesses the time periodicity, which is consistent with numerical results.Similar results are also obtained for the mixed initialboundary value problems with Dirichlet boundary conditions or Neumann boundary conditions.