TY - JOUR T1 - Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations JO - East Asian Journal on Applied Mathematics VL - 1 SP - 100 EP - 125 PY - 2018 DA - 2018/02 SN - 8 DO - http://doi.org/10.4208/eajam.020817.101017a UR - https://global-sci.org/intro/article_detail/eajam/10887.html KW - Discrete complex mKdV equation, modulational instability, generalised perturbation $(n, N-n)$-fold Darboux transformation, higher-order rogue wave solutions, higher-order rational soliton solutions. AB -

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.