So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. Bu...So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.展开更多
In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the ...In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106)
文摘So far, Lou＇s direct perturbation method has been applied successfully to solve the nonlinear SchrSdinger equation（NLSE） hierarchy, such as the NLSE, the coupled NLSE, the critical NLSE, and the derivative NLSE. But to our knowledge, this method for other types of perturbed nonlinear evolution equations has still been lacking. In this paper, Lou＇s direct perturbation method is applied to the study of perturbed complex Burgers equation. By this method, we calculate not only the zero-order adiabatic solution, but also the first order modification.
基金Project supported by the National Natural Science Foundation of China （Grant No 10575087） and the Natural Science Foundation of Zheiiang Province of China （Grant No 102053）. 0ne of the authors （Lin） would like to thank Prof. Sen-yue Lou for many useful discussions.
文摘In this paper Lou＇s direct perturbation method is applied to the perturbed coupled nonlinear Schrodinger equations to obtain their asymptotical solutions, which include not only the zero-order solutions but also the first-order modifications. Based on the asymptotical solutions, the effects of perturbations on soliton parameters and the collision between two solitons are then discussed in brief. Furthermore, we directly simulate the perturbed coupled nonlinear SchrSdinger equations by split-step Fourier method to check the validity of the direct perturbation method. It turns out that our analytical results are well supported by the numerical calculations.
