Novel localized wave of modified Kadomtsev–Petviashvili equation

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Ming Wang, Tao Xu, Guoliang He
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引用次数: 0

Abstract

In this paper, we investigate the data-driven localized solutions of Kadomtsev–Petviashvili (KP) and modified KP equation. Through the two-dimensional Miura transformation, the solutions of modified KP equation can be converted into the solutions of KP equation, but the process is not invertible in mathematics. Based on the neural network, the localized waves of modified KP equation are obtained under an unsupervised training with the aid of two-dimensional Miura transformation and the initial and boundary conditions of solution of the KP equation. As the result of the different hyperparameters, three types of localized waves are found after the training, including the shape of kink, dark and kink-bell. The evolution and error dynamics of the predicted solutions are analyzed through the graphics.

修正的卡多姆采夫-彼得维亚什维利方程的新局部波
本文研究了数据驱动的卡多姆采夫-彼得维亚什维利(KP)方程和修正 KP 方程的局部解。通过二维三浦变换,修正 KP 方程的解可以转化为 KP 方程的解,但这一过程在数学上是不可逆转的。基于神经网络,借助二维三浦变换和 KP 方程解的初始条件和边界条件,在无监督训练下得到修正 KP 方程的局部波。由于超参数的不同,训练后发现了三种类型的局部波,包括扭结波、暗波和扭结-贝尔波。通过图形分析了预测解的演变和误差动态。
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来源期刊
Wave Motion
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.
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