We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(...We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.展开更多
In this study, He's Energy Balance Method (EBM) was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffi...In this study, He's Energy Balance Method (EBM) was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffing oscillator equation is presented. For illustration of effectiveness and convenience of the EBM, different cases of cubic-quintic Duffing oscillator with different parameters of α,β and y were compared with the exact solution. We found that the solutions were valid for small as well as large amplitudes of oscillation. The results show that the EBM is very convenient and precise, so it can be widely appli- cable in engineering and other sciences.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10875106 and 11175158
文摘We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.
文摘In this study, He's Energy Balance Method (EBM) was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffing oscillator equation is presented. For illustration of effectiveness and convenience of the EBM, different cases of cubic-quintic Duffing oscillator with different parameters of α,β and y were compared with the exact solution. We found that the solutions were valid for small as well as large amplitudes of oscillation. The results show that the EBM is very convenient and precise, so it can be widely appli- cable in engineering and other sciences.