The non-linear Schrödinger equation associated with the soliton surfaces in Minkowski 3-space

Author:

Elsharkawy Ayman1,Cesarano Clemente2,Tawfiq Abdelrhman3,Ismail Abdul Aziz14

Affiliation:

1. Mathematics Department, Faculty of Science, Tanta University, 31511 Tanta, Egypt

2. Section of Mathematics, International Telematic University Uninettuno, 001186 Roma, Italy

3. Mathematics Department, Faculty of Education, Ain-Shams University, 11566 Cairo, Egypt

4. Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, 5555 Makkah, Saudi Arabia. Email: aiismail@uqu.edu.sa

Abstract

<abstract><p>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 $ \mathbb{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 $ \mathbb{E}_1^3 $ are examined and the Gaussian and mean curvatures for each case are determined. The quasi-Hasimoto surfaces in $ \mathbb{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 $ \mathbb{E}_1^3 $ is described. Thus, the $ s $-parameter and $ t $-parameter curves of quasi-Hasimoto surfaces in $ \mathbb{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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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