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 Schrödinger 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.