# American Institute of Mathematical Sciences

October  1999, 5(4): 729-740. doi: 10.3934/dcds.1999.5.729

## Smooth solution of the generalized system of ferro-magnetic chain

 1 Institute of Applied Physics & Computational Math., Beijing 100088, China 2 Dept. of Math., Beijing Normal University, Beijing, 100875, China

Received  August 1998 Revised  April 1999 Published  July 1999

In this paper, we consider the initial value problem with periodic boundary condition for a class of general systems of the ferromagnetic chain

$z_t=-\alpha z\times (z\times z_{x x})+ z\times z_{x x}+z\times f(z), \qquad (\alpha \geq 0).$

The existence of unique smooth solutions is proved by using the technique of spatial difference and a priori estimates of higher-order derivatives in Sobolev spaces.

Citation: Boling Guo, Haiyang Huang. Smooth solution of the generalized system of ferro-magnetic chain. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 729-740. doi: 10.3934/dcds.1999.5.729
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