Geometric connections between curves in euclidean space and hirota equation

This study, prepared as a master's thesis, consists of four chapters. Chapter 1, i.e., the introduction, gives a brief description of what the study is based on and what its aim is.Chapter 2 provides basic definitions in the Euclidean space and formulates the relationship between curves and partial differentialequations.Section 3 provides a relationship between the tangent, normal, and binormal of three distinct curves in Euclidean space and the Hirota equation, provided that these curves satisfy the Extended Landau-Lifshitz (GLL) equation. Finally, the conclusion provides instructions on how to derive the NLS and mKdV equations through the consideration of specific scenarios.