研究sine-Gordon方程的极限对称及应用.由对称引出相似约化,求得sine-Gordon 方程的极限解;利用对称与孤子方程的自相容源之间的联系,得到带新自相容源的sine-Gordon方程,并求出该方程的解.

Limit symmetry of the sine-Gordon equation and its applications are considered. The similarity reduction leads to limit solutions of the sineGordon equation. Besides, based on the relationship between symmetries and sources of soliton equations, a sine-Gordon equation with new selfconsistent sources is obtained and its solutions are derived.