K(m，n，P)方程多-Compacton相互作用的数值研究  

Numerical investigation on the interaction between multi-compacton of K(m,n,p) equation

作　　者：王光辉[1] 王林雪[1] 王灯山[2] 刘丛波[1] 石玉仁[1] 

机构地区：[1]西北师范大学物理与电子工程学院,兰州730070 [2]北京信息科技大学理学院,北京100192

出　　处：《物理学报》2014年第18期61-68,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11047010,11001263,11375030);北京市自然科学基金(批准号:1132016);北京市科技新星计划(批准号:Z131109000413029)资助的课题~~

摘　　要：采用有限差分法对非线性色散K(m,n,p)方程的多-Compacton之间的相互作用进行了数值研究.该差分方法为二阶精度且线性意义下绝对稳定的无耗散格式,通过添加人工耗散项有效防止了数值解的爆破现象.首先对单-Compacton的长时间演化行为进行了数值模拟,验证了数值方法的有效性.然后对双-CompaCton和三-Compacton的碰撞过程进行了数值研究,发现多-Compacton碰撞之后基本保持碰撞之前的波形和波速,但在波后产生小振幅的Compacton-Anticompacton对.We numerically investigate the interaction between multi-compactons of the K（m, n, p） equation by a finite difference scheme that is of the second-order accuracy and absolutely stable in linearization sense. By adding an artificial dissipation term, it works well for preventing the break-up phenomena of the numerical solutions. Firstly, we simulate the long-time evolution behaviors of the single-compacton to verify the validity of the numerical method. It is shown that the numerical method is effective for solving this problem. Secondly, we study the nonlinear interaction between two-compacton and three-compacton by this numerical method. The numerical results indicate that the wave-frame and wave-velocity after collision are nearly the same as before collision. However, compacton-anticompacton pair induced behind the wave arises with small amplitudes.

关 键 词：K(m n p)方程 COMPACTON 有限差分法 

分 类 号：O241.82[理学—计算数学]