改进Boussinesq方程的改进五次三角b样条微分求积分法

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2025-09-26 DOI:10.1016/j.chaos.2025.117258

Jiawen Deng , Shahid Hussain , Kaysar Rahman

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引用次数: 0

摘要

本文提出了一种改进的五次三角b样条函数，并将其应用于微分求积法中来求解改进的Boussinesq方程，该方程是浅水波浪和非线性波浪现象的关键模型。通过特征值图分析稳定性。该方法成功地模拟了单波和双波孤波解，结果与所建立的数值方法和精确解进行了验证，证实了其有效性。此外，还探讨了孤波分裂运动、双孤波相互作用、多孤波相互运动等物理现象。这些发现突出了该方法在捕获孤立波的复杂行为方面的有效性，为非线性波动力学的研究提供了有价值的工具。

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Modified quintic trigonometric B-spline differential quadrature method for the improved Boussinesq equation

This study proposed a modified quintic trigonometric B-spline function applied within a differential quadrature method to solve the Improved Boussinesq equation, a key model for shallow water waves and nonlinear wave phenomena. Stability is analyzed through eigenvalue plots. The proposed technique successfully simulates both single and double solitary wave solutions, with results validated against established numerical methods and exact solutions, confirming its effectiveness. Additionally, the study explores physical phenomena such as Solitary wave splitting motion, interactions of double solitary waves, and mutual motion of multiple solitary waves. The findings highlight the method’s effectiveness in capturing the complex behaviors of solitary waves, serving as a valuable tool for research in nonlinear wave dynamics.

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.