University of Guilan Journal of Mathematical Modeling 2345-394X 13 1 2025 03 01 Lump wave dynamics and interaction analysis for an extended (2+1)-dimensional Kadomtsev-Petviashvili equation 17 32 8013 10.22124/jmm.2024.27798.2449 EN Majid Madadi Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45137-66731, Zanjan, Iran Esmaeel Asadi Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45137-66731, Zanjan, Iran & School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran Journal Article 2024 07 01 Constructing exact solutions for high-dimensional nonlinear evolution equations and exploring their dynamics are critical challenges with significant practical implications. The extended Kadomtsev-Petviashvili (eKP) equation, a key example of an integrable two-dimensional equation, highlights the importance of these studies. A logical extension is to investigate lump wave solutions in this context. In this paper, we introduce novel constrained conditions into $N-$soliton solutions for a $(2+1)$-dimensional eKP equation. We present a theorem to analyze the asymptotic behavior of the \( N \)-soliton solution. This analysis leads to the derivation of lump waves, along with the determination of their trajectories and velocities. To investigate the interaction between higher-order lumps and soliton waves, as well as breather waves, we employ the long wave limit method. We analyze the trajectory equations governing the motion before and after the collision of lumps and other waves and identify conditions under which the lump wave avoids collision with other waves. Several figures are included to illustrate the physical behavior of these solutions. https://jmm.guilan.ac.ir/article_8013_1e7822f8ecf3c334450ab2850c74b638.pdf