Moving non-null curves according to Bishop frame in Minkowski 3-space

Abstract

In this paper, we introduce three new transformations and establish connections between moving non-null curves and soliton equations according to Bishop frame in Minkowski 3-space. Later we find formulas for differentials of these three new transformations associated with the nonlinear heat system and repulsive type nonlinear Schrödinger equation.

Pseudo‐solitonic magnetic flows associated with nonlinear integrable systems in the Minkowski 3‐space

“…Gürbüz [48] concluded that if the flow of the curve 𝛼(s, u) is governed by the Landau-Lifshitz equation, which is given by ( 1 ) t =  1 ×  ( 1 ) ss , then the kinematics of the spacelike evolving curve 𝛼(s, u) are written by 𝜕 𝜕s…”

Hasimoto surfaces for two classes of curve evolution in Minkowski 3-space

“…Recently, some geometers studied connections between moving frame of space curves and soliton equations in ambient spaces (see [4][5][6][7][8][9][10][11][12][13]).…”

“…The differential formulas of Hasimoto transformations in Euclidean 3-space have been presented by Langer and Perline [4]. For the extension to the Lorentz version, Gürbüz suggested three classes of curve evolution associated with the nonlinear Schrödinger equation in Minkowski 3-space (see [6,8,9,12]). Also, 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.…”

Three Anholonomy Densities According to Bishop Frame in Euclidean 3-Space

“…Munijara and Lakshmanan investigated the motion of space curves in a three-dimensional Minkowski space [20]. Gürbüz studied three classes of curve evolution in terms of Bishop frame in Minkowski 3-space [10]. Guha studied the connection of moving space curves with KdV-type equations in Euclidean 3-space [9].…”