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On a Hirota equation in oceanic fluid mechanics: Double-pole breather-to-soliton transitions

Author

Listed:
  • Wu, Xi-Hu
  • Gao, Yi-Tian
  • Yu, Xin

Abstract

In oceanic fluid mechanics, a Hirota equation describing the propagation of the deep ocean broader-banded waves is studied in this paper. With respect to the envelope of the wave field, we simultaneously take the multi-pole phenomena and breather-to-soliton transitions into account to investigate the double-pole breather-to-soliton transitions via the second-order generalized Darboux transformation. Under certain parameter conditions, double-pole anti-dark solitons, periodic waves, W-shaped solitons and multi-peak solitons are derived, analyzed and graphically illustrated. We perform the asymptotic analysis on the double-pole anti-dark solitons to investigate their interaction properties, e.g., amplitudes, characteristic lines, slopes, phase shifts and position differences. Different from the known double-pole solitons of some other models, the double-pole anti-dark solitons, hereby, indicate that the two soliton components own unequal amplitudes.

Suggested Citation

  • Wu, Xi-Hu & Gao, Yi-Tian & Yu, Xin, 2024. "On a Hirota equation in oceanic fluid mechanics: Double-pole breather-to-soliton transitions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004260
    DOI: 10.1016/j.chaos.2024.114874
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