Lump wave dynamics and interaction analysis for an extended (2+1)-dimensional Kadomtsev-Petviashvili equation

Madadi, Majid; Asadi, Esmaeel

doi:10.22124/jmm.2024.27798.2449

Lump wave dynamics and interaction analysis for an extended (2+1)-dimensional Kadomtsev-Petviashvili equation

Document Type : Research Article

Authors

Majid Madadi ¹
Esmaeel Asadi ²

¹ Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45137-66731, Zanjan, Iran

² 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

10.22124/jmm.2024.27798.2449

Abstract

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.

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