Decaying solitary waves propagating in one-dimensional damped granular chain

We numerically investigate the nonlinear waves propagating in a one-dimensional particle chain when the damping effect is taken into account. It is found that decaying solitary waves exist, in which the amplitude of the wave decreases exponentially as time increases. Meanwhile, the velocity of the solitary wave also slows down as time goes. This result implies that the damping coefficient is an important parameter in such a nonlinear system. Theoretical analysis has also been done by the reductive perturbation method. The result indicates that the nonlinear waves propagating in such a system can be described by the damped KdV equation.     

KdV-Burgers方程行波解的稳定性

对KdV-Burgers方程的行波解进行线性稳定性分析，数值结果表明：对于正耗散情形，其行波解是稳定的；对于负耗散情形，其行波解是不稳定的.其次构造有限差分法对其行波解进行非线性动力学演化，结果表明：对于正耗散情形，KdV-Burgers方程的行波解是稳定的.本文结果修正和完善了相关文献中所得结论.