@article{Elsharkawy2022, 
author = {Ayman Elsharkawy and Clemente Cesarano and Abdelrhman Tawfiq and Abdul Aziz Ismail},
title = {The non-linear Schrödinger equation associated with the soliton surfaces in Minkowski 3-space},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {17879-17893},
keywords = {Minkowski space, Hasimoto surfaces, smoke ring equation, Gaussian and mean curvatures},
url = {https://www.sciopen.com/article/10.3934/math.2022985},
doi = {10.3934/math.2022985},
abstract = {The quasi frame is more efficient than the Frenet frame in investigating surfaces, and it is regarded a generalization frame of both the Frenet and Bishop frames. The geometry of quasi-Hasimoto surfaces in Minkowski 3-space              E        1    3   is investigated in this paper. For the three situations of non-lightlike curves, the geometric features of the quasi-Hasimoto surfaces in              E        1    3   are examined and the Gaussian and mean curvatures for each case are determined. The quasi-Hasimoto surfaces in              E        1    3   must satisfy a necessary and sufficient condition to be developable surfaces. As a result, the parameter curves of quasi-Hasimoto surfaces in              E        1    3   is described. Thus, the    s-parameter and    t-parameter curves of quasi-Hasimoto surfaces in              E        1    3   are said to be geodesics, asymptotic, and curvature lines under necessary and sufficient circumstances are proved. Finally, quasi curves and associated quasi-Hasimoto surface correspondences are discussed.}
}