Abstract
AbstractIn this work, we study Hasimoto surfaces for the second and third classes of curve evolution corresponding to a Frenet frame in Minkowski 3-space. Later, we derive two formulas for the differentials of the second and third Hasimoto-like transformations associated with the repulsive-type nonlinear Schrödinger equation.
Highlights
Many mathematicians have been interested for a long time in studying connections between integrable equations and geometric motions of a curve in various spaces
Lamb [3] introduced the Hasimoto transformation as a complex function and he studied a certain class of moving space curves with soliton equations
The differential formulas of Hasimoto transformations in Euclidean 3-space have been presented by Langer and Perline [4]
Summary
Many mathematicians have been interested for a long time in studying connections between integrable equations (soliton equations) and geometric motions of a curve in various spaces. Lamb [3] introduced the Hasimoto transformation as a complex function and he studied a certain class of moving space curves with soliton equations. Murugesh and Balakrishnan [5] presented two Hasimoto transformations as two other complex functions They showed that there are two other classes of curve evolution that may be so identified. Gürbüz [6] extended the results of Langer and Perline in [4] in Minkowski 3-space, and she derived differential formulas of Hasimoto transformations for the first class of curve evolutions associated with the repulsive-type nonlinear Schrödinger equation in Minkowski 3-space. We give differential formulas of two Hasimoto-like transformations of the second and third classes associated with the repulsive-type nonlinear Schrödinger equation in Minkowski 3-space
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