East Asian J. Appl. Math., 8 (2018), pp. 100-125.
Published online: 2018-02
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The generalised perturbation $(n, N−n)$-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations. The structure of such waves and details of their evolution are investigated via numerical simulations, showing that the strong interaction yields weak oscillation and stability whereas the weak interaction is associated with strong oscillation and instability. A small noise has a weak influence on the wave propagation for the strong interaction, but substantially changes the wave behaviour in the weak interaction case.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.020817.101017a}, url = {http://global-sci.org/intro/article_detail/eajam/10887.html} }The generalised perturbation $(n, N−n)$-fold Darboux transformation is used to derive new higher-order rogue wave and rational soliton solutions of the discrete complex mKdV equations. The structure of such waves and details of their evolution are investigated via numerical simulations, showing that the strong interaction yields weak oscillation and stability whereas the weak interaction is associated with strong oscillation and instability. A small noise has a weak influence on the wave propagation for the strong interaction, but substantially changes the wave behaviour in the weak interaction case.