Solitonic hybrid magnetic parallel transportation and energy distribution flows in minkowski space

Abstract

This paper primarily focuses on the development of a novel category of magnetic curves. While we explore conventional techniques, viewing these curves through a geometric lens and considering the electromagnetic principles of physics, our emphasis shifts towards investigating integrability conditions and solitonic behaviors. Consequently, we introduce diverse varieties of hybrid magnetic curves linked to the modified non-linear Schrodinger (mNLS) equation within the context of three-dimensional Minkowski space. We also scrutinize alterations in energy distribution and the pseudo-parallel transport of magnetic and electric vector lines associated with flows, enabling the construction of a new class of hybrid magnetic soliton surfaces. Finally, we employ the conformable fractional method to derive specific solution families for these integrable systems, presenting them visually.