二维空间旋转孤立波的相互作用

INTERACTION OF ROTATING SOLITARY WAVES IN TWO-DIMENSIONAL SPACES

利用图形分析方法对(2+1)维频散长波方程的旋转孤立波之间的相互作用进行了详细分析,发现了旋转孤立波相互作用产生的一些新的重要非线性现象.这就是,两个旋转孤立波的碰撞是完全非弹性的,它们碰撞之后可以合并成一个旋转孤立波或一个不旋转孤立波,同时可以发生波形转换及性质改变等现象.这些现象的发现,对非线性水波传播与相互作用规律的进一步认识、对非线性水波的控制与利用都具有重要的理论意义.

Using the method of figure-analysis, we investigated the interaction between rotating solitary waves for （2 ＋ 1 ） -dimensional dispersive long-wave equations, and found some new nonlinear phenomena of rotating solitary wave interactions. These phenomena are ： （ 1 ） the interaction between rotating solitary waves is completely non-elastic, （2） two rotating solitary waves may merge into one rotating solitary wave or one non-rotating solitary wave through the collision, and at the same time waveform conversion or property change of solitary wave may happen.