riemann solitons on the peres metric

In this paper, we investigate the existence of riemann solitons in the peres metric, a four-dimensional lorentzian pp-wave spacetime. after recalling the definition of riemann solitons and the curvature properties of this metric, we derive the determining equations for the potential soliton vector fields and obtain these vector fields. this analysis shows that the null wave nature of the peres metric naturally supports stable soliton structures. this study contributes to the understanding of riemann solitons in lorentzian geometry and their role in mathematical physics.