Abstract
In this research, we delve into the study of Riemann solitons within the context of Lorentzian pr-wave manifolds. Our investigation aims to systematically classify all vector fields that are associated with Riemann solitons on these specific manifolds. A significant aspect of our work is to identify which of these vector fields can be categorized as the gradient type. Furthermore, we demonstrate that any vector field that has the potential to be linked with Riemann solitons can be classified into several categories, namely, Ricci bi-conformal, Killing, and Ricci collineation vector fields. This classification not only enhances our understanding of the geometric properties of these manifolds but also sheds light on the intricate relationships between the various types of vector fields and Riemann solitons. The analysis also gives explicit conditions for the steady and non-steady cases. Gradient Riemann solitons occur only in the steady case, while the potential vector fields may additionally be Killing, Ricci collineation, or Ricci bi-conformal vector fields.