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The canonical AB system: conservation laws and soliton solutions

Author

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  • Guo, Rui
  • Liu, Yue-Feng

Abstract

Under investigation in this paper is the canonical AB system, which describes the marginally unstable baroclinic wave packets in the geophysical fluids and ultra-short pulses in nonlinear optics. Through symbolic computation, conservation laws are derived. Furthermore, by virtue of the Darboux transformation, the explicit multi-soliton solutions are generated. Figures are plotted to reveal the following dynamic features of the solitons: (1) Elastic interactions of two one-peak bright solitons, of two one-peak dark solitons and of two two-peak dark solitons; (2) Parallel propagations of two one-peak bright solitons, of two one-peak dark solitons and of two two-peak dark solitons; (3) Propagations of three types of bound solitons: periodic propagation of bound solitons taking on contrary trends, mutual attractions and repulsions of two bight bound solitons and of two dark bound solitons.

Suggested Citation

  • Guo, Rui & Liu, Yue-Feng, 2015. "The canonical AB system: conservation laws and soliton solutions," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 153-163.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:153-163
    DOI: 10.1016/j.amc.2015.02.028
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