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

Document Type : Research Article

Authors

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

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.

Keywords

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References

[1] M.J. Ablowitz, J. Satsuma, Solitons and rational solutions of nonlinear evolution equations, J.
Math. Phys. 19 (1978) 2180–2186.
[2] L. Akinyemi, Shallow ocean soliton and localized waves in extended (2+ 1)-dimensional nonlinear
evolution equations, Phys. Lett. A. 463 (2023) 1–24.
[3] J.S. Chen, Y. Hang, X. L¨u, Elastic collision between one lump wave and multiple stripe waves of
nonlinear evolution equations, Commun. Nonlinear Sci. Numer. Simul. 130 (2024) 1–17.
[4] A.S. Fokas, Integrable nonlinear evolution partial differential equations in 4+ 2 and 3+ 1 dimen-
sions, Phys. Rev. Lett. 96 (2006) 1–9.
[5] M.S. Hashemi, A variable coefficient third degree generalized Abel equation method for solving
stochastic Schr¨odinger–Hirota model, Chaos Solitons Fractals. 180 (2024) 1–8.
[6] R. Hirota, Exact solution of the Kortewegde Vries equation for multiple collisions of solitons, Phys.
Rev. Lett. 27 (1971) 19–28.
[7] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, 2004.
[8] I.M. Tarikul, M.A. Akter, S. Ryehan, J.F. G´omez, M.D. Akbar, A variety of solitons on the oceans
exposed by the Kadomtsev Petviashvili-modified equal width equation adopting different tech-
niques, J. Ocean Engin. Sci. 7 (2022) 528–535.
[9] S. Kumar, B. Mohan, A generalized nonlinear fifth-order KdV-type equation with multiple soliton
solutions: Painlev´e analysis and Hirota Bilinear technique, Phys. Scr. 97 (2022) 123–132.
[10] Y. Li, X. Hao, R. Yao, Y. Xia, Y. Shen, Nonlinear superposition among lump soliton, stripe soli-
tons and other nonlinear localized waves of the (2+ 1)-dimensional cpKP-BKP equation, Math.
Comput. Simul. 208 (2023) 57–70.
[11] W.X. Ma, Y. Huang, F. Wang, Inverse scattering transforms and soliton solutions of nonlocal
reverse-space nonlinear Schr¨odinger hierarchies, Stud. Appl. Math. 145 (2020) 563–585.
[12] M. Madadi, E. Asadi, B. Ghanbari, Resonant Y-Type solutions, N-Lump waves, and hybrid solutions
to a Ma-type model: a study of lump wave trajectories in superposition, Phys. Scr. 98 (2023) 12–36.
[13] S. Mahmood, H. Ur-Rehman, Existence and propagation characteristics of ion-acoustic
Kadomtsev–Petviashvili (KP) solitons in nonthermal multi-ion plasmas with kappa distributed elec-
trons, Chaos Solitons Fractals. 169 (2023) 1–13.
[14] Y. Ohta, Yasuhiro, J. Yang, General high-order rogue waves and their dynamics in the nonlinear
Schr¨odinger equation, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 468 (2012) 1716–1740.
[15] Z. Qi, Q. Chen, M. Wang, B. Li, New mixed solutions generated by velocity resonance in the (2+
1)-dimensional Sawada–Kotera equation, Nonlinear Dynam. 108 (2022) 1617–1626.
[16] S. Wang, Novel soliton solutions of CNLSEs with Hirota bilinear method, J. Opt. 54 (2023) 1–6.
[17] A.M. Wazwaz, Breather wave solutions for an integrable (3+ 1)-dimensional combined pKP–BKP
equation, Chaos Solitons Fractals. 182 (2024) 1–14.
[18] X.H. Wu, Y.T. Gao, Generalized Darboux transformation and solitons for the Ablowitz–Ladik equa-
tion in an electrical lattice, Appl. Math. Lett. 137 (2023) 108–122.
[19] K.J. Wang, Dynamics of complexiton, Y-type soliton and interaction solutions to the (3+1)-
dimensional Kudryashov-Sinelshchikov equation in liquid with gas bubbles, Nonlinear Dynam. 54
(2023) 1–9.
[20] Z. Zhang, X. Yang, W. Li, B. Li, Trajectory equation of a lump before and after collision with line,
lump, and breather waves for (2+ 1)-dimensional Kadomtsev–Petviashvili equation, Chin. Phys. B.
28, (2019), 1–18.
Journal of Mathematical Modeling
Volume 13, Issue 1
March 2025
Pages 17-32

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