（3+1）维b型Kadomtsev-Petviashvili方程的动态渐近分析：双线性向量法下有理解与相互作用解的叠加公式

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-08-14 DOI:10.1016/j.matcom.2025.07.058

Hangbing Shao , Sudao Bilige

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引用次数: 0

摘要

得到了基于Hirota双线性形式的（3+1）维b型Kadomtsev-Petviashvili方程的有理解和两类交互解。同时，独立提出了双线性向量法。双线性矢量法将计算机符号计算与人工逻辑推导相结合，便于叠加公式的获取。三种类型的解表现出不同的动力学行为，它们可以基于渐近分析得到。特别是，两种类型的交互解决方案在空间全局性上存在差异。图解地说明了有理波的稳定性以及有理波与条纹波的碰撞行为。

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Dynamical asymptotic analysis to a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: The superposition formulas of rational solutions and interaction solutions under the bilinear vector method

We obtain rational solutions and two types of interaction solutions for a (3+1)-dimensional B-type Kadomtsev–Petviashvili equation based on the Hirota bilinear form. Meanwhile, the bilinear vector method is independently proposed. The bilinear vector method combines computer symbol calculation and manual logic deduction, making it easy to acquire the superposition formula. Three types of solutions exhibit different dynamical behaviors, and they can be obtained based on asymptotic analysis. Especially, two types of interaction solutions differ in spatial globality. The stability of the rational wave as well as the collision behavior of the rational wave and stripe waves are both graphically shown.

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.