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

Abstract

In this paper, we introduce a novel class of magnetic curves and call it pseudo-solitonic magnetic curves by considering the connection between two significant types of integrable equations, that is, the nonlinear heat system/the nonlinear Schrodinger equation and moving space curves in the Minkowski 3-space. Later, we construct a very special class of soliton surfaces and call it pseudo-solitonic magnetic surfaces by considering the effects of the pseudo-solitonic magnetic flows in the Minkowski 3-space. These curves and surfaces are very useful since they not only contain geometric and physical features in their inner forms but also their constructions rely on a simple geometric procedure compared to other models.