Madadi, MajidHosseini, KamyarAhmad, Shabir2026-04-212026-04-2120262190-544410.1140/epjp/s13360-026-07525-82-s2.0-105033457666https://hdl.handle.net/123456789/9073https://doi.org/10.1140/epjp/s13360-026-07525-8In this work, we consider a generalized extended Kadomtsev-Petviashvili (geKP) equation that contains higher order temporal dispersion and mixed derivative terms. This form of the KP equation provides a wider setting for studying nonlinear waves in areas such as fluids, plasmas, and optics. We first test the integrability of the system by using the Painlev & eacute; analysis and by constructing multi-soliton solutions, which both lead to the same constraint on the equation's parameters. On this basis, we study rogue wave (RW) solutions in two ways. A direct symbolic computation method gives higher order rational solutions and also allows us to introduce center-controlled RWs, in which additional parameters can shift and arrange the wave peaks. In parallel, we apply the KP hierarchy reduction method, which produces determinant form rational solutions and clarifies the algebraic structure behind the system. The obtained rational solutions correspond to line-type RWs, which are localized along an oblique direction in the (x, y) plane while remaining invariant along the transverse direction. The comparison shows that the symbolic solutions appear as special cases of the KP reduction approach. Several examples and plots are given to illustrate the dynamics.eninfo:eu-repo/semantics/closedAccessArticle