A different modelling of complex Hasimoto map for pseudo-null curves via Bishop frame

Abstract

In this paper, we construct some links between visco model of motion and equations attained by taking geometric differential description of Hasimoto map of pseudo-null curves framed by the Bishop frame and some physical consequences. First, we find that the equations of Hasimoto transformation are occurred by adapting Hasimoto map for pseudo-null curves. Then, we investigate the correspondence of both the Landau–Lifshitz system and the vortex filament equation by means of the Hasimoto map of pseudo-null curves. Lastly, we portray the links of findings obtained by geometric physical issues. Finally, we simulate optical solutions with graphically physical constructions.

Keywords:

• Complex Hasimoto map
• Bishop frame of pseudo-null curve
• Landau–Lifshitz system
• vortex filament flow
• complex vector field
• visco model

AMS Subject Classifications:

• 53A04
• 76B47
• 34A34

Acknowledgement

The authors express thanks to the referees who contributed to the improvement of the work by their valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).