https://doi.org/10.1140/epjp/s13360-026-07525-8
Regular Article
Oblique line rogue wave solutions of the generalized extended KP equation: from bilinear forms to KP hierarchy
1
Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan
2
Department of Mathematics, Near East University TRNC, Mersin 10, 99138, Nicosia, Turkey
3
Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, 602105, Chennai, Tamilnadu, India
4
Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
5
Department of Mathematics and Physics, University of Campania “Luigi Vanvitelli”, 81100, Caserta, Italy
a
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Received:
29
October
2025
Accepted:
2
March
2026
Published online:
11
March
2026
Abstract
In 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 Painlevé 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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
