摘要
The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations shave some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.
The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations shave some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.
基金
Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106)
