Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubicben quintic Grossben Pitaevskii equation |
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Authors: | Dai Chao-Qing Chen Rui-Pin and Wang Yue-Yue |
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Institution: | School of Sciences, Zhejiang Agricultural and Forestry University, Linán 311300, China;School of Sciences, Zhejiang Agricultural and Forestry University, Linán 311300, China;School of Sciences, Zhejiang Agricultural and Forestry University, Linán 311300, China |
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Abstract: | With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system. |
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Keywords: | Gross-Pitaevskii equation similarity transformation self-similar solutions |
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