Lump chains in the BKP equation

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-06-06 DOI:10.1016/j.cnsns.2025.108982

Shoufeng Shen , Han-Han Sheng , Guo-Fu Yu , Kai Zhou

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引用次数: 0

Abstract

In this paper, we investigate a broad class of solutions of the B-type Kadomtseve-Petviashvili (BKP) equation by utilizing the Pfaffian

τ

-function. The fundamental solution is a linear periodic chain of lumps moving at separate group and wave velocities. We construct general linear arrangements for the BKP equation and give degenerate configurations such as parallel and superimposed lump chains. The soliton-breather resonant solutions are derived, and interaction asymptotic analyses are performed. It is shown that one soliton can split into a new soliton and a breather, or one soliton and one breather merge into a new soliton. Resonant interactions of lump chains are analyzed with asymptotic analysis. We find

Y

-shaped lump chains where one lump chain splits into two parallel lump chains, or two parallel lump chains merge into a new one. Multi-lump chains are constructed with polygonal interaction regions. Hybrid solutions consisting of lump chains and individual lumps are found.

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BKP方程中的块链

本文利用Pfaffian τ函数研究了b型Kadomtseve-Petviashvili （BKP）方程的一类广义解。基本解是一个以不同群速和波速运动的块的线性周期链。我们构造了BKP方程的一般线性排列，并给出了退化构型，如平行和叠加块链。导出了孤子-呼吸子共振解，并进行了相互作用渐近分析。证明了一个孤子可以分裂成一个新孤子和一个呼吸子，或者一个孤子和一个呼吸子合并成一个新孤子。用渐近分析法分析了块状链的共振相互作用。我们发现y型块状链，其中一个块状链分裂成两个平行的块状链，或者两个平行的块状链合并成一个新的块状链。用多边形相互作用区域构造多块链。得到由块链和单个块组成的混合解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.