Volume 8, Issue 1
Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations

Xiao-Yong Wen

East Asian J. Appl. Math., 8 (2018), pp. 100-125.

Published online: 2018-02

Preview Full PDF 409 1833
Export citation
  • Abstract

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.

  • Keywords

Discrete complex mKdV equation modulational instability generalised perturbation $(n N-n)$-fold Darboux transformation higher-order rogue wave solutions higher-order rational soliton solutions

  • AMS Subject Headings

35Q51 35Q53 37K05 37K10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-8-100, author = {Xiao-Yong Wen}, title = {Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {1}, pages = {100--125}, abstract = {

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

Xiao-Yong Wen. (1970). Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations. East Asian Journal on Applied Mathematics. 8 (1). 100-125. doi:10.4208/eajam.020817.101017a
Copy to clipboard
The citation has been copied to your clipboard