所有一、二阶（2+1）维非线性波动方程均由理想流体模型的欧拉方程导出，并给出了它们的行波解

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2024-12-16 DOI:10.1016/j.wavemoti.2024.103477

Piotr Rozmej , Anna Karczewska

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引用次数: 0

摘要

我们回顾了我们最近从理想流体模型中导出的（2+1）维非线性波动方程。这些是KdV的扩展，五阶KdV， Gardner，扩展KdV和扩展KP方程到两个空间维度。我们以行波的形式讨论了这些方程的解析解。所有这些解，孤子解、余弦解和叠加解，都类似于相应的（1+1）维方程的解。本文首次导出了完整的（2+1）维五阶KdV方程、（2+1）维Gardner方程及其孤子解。

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All first- and second-order (2+1)-dimensional nonlinear wave equations derived from the Euler equations for an ideal fluid model and their traveling wave solutions

We review the (2+1)-dimensional nonlinear wave equations we recently derived from the ideal fluid model. These are extensions of the KdV, fifth-order KdV, Gardner, extended KdV and extended KP equations into two spatial dimensions. We discuss analytical solutions to these equations in the form of traveling waves. All these solutions, soliton, cnoidal, and superposition ones, are analogous to solutions of the corresponding (1+1)-dimensional equations. The complete (2+1)-dimensional fifth-order KdV equation, (2+1)-dimensional Gardner equation, and their soliton solutions are derived here for the first time.

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.