A new version of the motion equations of pseudo null curves with compatible Hasimoto map

Abstract

In this manuscript, we study links between nonlinear equations of motion and equations attained by taking geometric differential description of Hasimoto map of pseudo null curves and some physical consequences. First, we find the equations of Hasimoto transformation occurred by adapting Hasimoto map for pseudo null curves. Then, we investigate the correspondence of both Landau-Lifshitz system and vortex filament equation by means of the Hasimoto map of pseudo null curves. Moreover, we design the links of findings obtained by geometric physical issues. Finally, optical solutions are simulated by graphically physical constructions with Khater method to obtain optical solutions of fractional order differential equations.