论文标题
sublinear KDV方程中紧凑型物的稳定性和相互作用
Stability and interaction of compactons in the sublinear KdV equation
论文作者
论文摘要
在具有sublinear非线性的Korteweg-De Vries（KDV）方程的框架中研究了压实子。压实子代表两极分性的局部钟形波，其传播与线性KDV方程的波相同。它们的振幅和宽度与它们的速度成正比。紧凑型相对于对称紧凑的扰动的能量稳定性在分析中得到证明。对压缩物的动力学进行了数值研究，包括脉搏样干扰的演变以及相同或相反极性的压实物的相互作用。紧凑型物质上的相互作用，尽管碰撞后几乎恢复了它们的形状。紧凑型物质在悠久的孤子状结构和传播波能的小规模波中起着两倍的作用。
Compactons are studied in the framework of the Korteweg-de Vries (KdV) equation with the sublinear nonlinearity. Compactons represent localized bell-shaped waves of either polarity which propagate to the same direction as waves of the linear KdV equation. Their amplitude and width are inverse proportional to their speed. The energetic stability of compactons with respect to symmetric compact perturbations with the same support is proven analytically. Dynamics of compactons is studied numerically, including evolution of pulse-like disturbances and interactions of compactons of the same or opposite polarities. Compactons interact inelastically, though almost restore their shapes after collisions. Compactons play a two-fold role of the long-living soliton-like structures and of the small-scale waves which spread the wave energy.
