Diverse Soliton wave solutions of for the nonlinear potential Kadomtsev-Petviashvili and Calogero-Degasperis equations
Diverse Soliton wave solutions of for the nonlinear potential Kadomtsev-Petviashvili and Calogero-Degasperis equations
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DOI：
10.1016/j.rinp.2021.105116
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发表时间：
2022-01-07
影响因子：
5.3
通讯作者：
Lu, Dianchen
中科院分区：
文献类型：
--
作者：
Khater, Mostafa M. A.;Lu, Dianchen
本文用直接代数方法研究了非线性势场Kadomtsev-Petviashvili和Calogero-DeGasperis方程的孤子波结构。利用这些方程研究了沿y轴传播的Riemann波与沿x轴传播的长波的(2+1)维相互作用，以及KdV方程在横向微扰下单孤子解的稳定性。由于弱色散的非线性波的波长大于其振幅，且其在二维空间(重标度y)上的变化慢于在主传播方向(重标度x)上的变化，因此所研究模型的孤子波解被用来描述波动动力学。通过在二维、三维和等高线上绘制它们，可以获得并演示许多解决方案。实现的分析方案的性能验证了其有效性和有效性。所有解决方案的准确性都是通过将它们放回原始模型来检查的。
This paper investigates the soliton wave structures of the nonlinear potential Kadomtsev-Petviashvili and Calogero-Degasperis equations by employing the direct algebraic method. These equations are used to investigate the (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis and the stability of the one-soliton solution of the well-known Korteweg-de Vries (KdV) equation under transverse perturbations. Since the wavelength of weakly dispersive, nonlinear waves is longer than their amplitude and their variations in the second spatial dimension (rescaled y) are slower than those in the principal propagation direction (rescaled x), the studied models' soliton wave solutions are used to describe wave dynamics. Many solutions are obtained and demonstrated by plotting them in 2D, 3D, and contour plots. The implemented analytical scheme's performance verifies its effectiveness and power. All solutions' accuracy is checked by putting them back into their original model.