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Wave propagation of resonance multi-stripes, complexitons, and lump and its variety interaction solutions to the (2+1)-dimensional pKP equation
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2021-04-19 , DOI: 10.1016/j.cnsns.2021.105853
Dipankar Kumar , Chun-Ku Kuo , Gour Chandra Paul , Jui Saha , Israt Jahan

This study deals with the (2+1)-dimensional potential Kadomtsev-Petviashvili (pKP) equation, which is used to describe the dynamics of a wave of small but finite amplitude in two dimensions in diverse areas of physics and applied mathematics. Through symbolic computations with Maple, the resonance multi-stripe solutions in real fields, and multi-stripe complexiton solutions in complex fields are derived via the simplified linear superposition principle in conjunction with Hirota's bilinear method (HBM). Furthermore, lump, lump-stripe, and lump-triangular periodic wave solutions are derived by employing the HBM. A positive quadratic function with exponential, hyperbolic cosine and trigonometric cosine functions are considered to reach such aims. For lump solutions, it is found that the shape and amplitude of a lump wave remain unchanged during its propagation. On the other hand, lump-stripe interaction solitons present the fission and fusion interaction phenomena between the lump and stripe solitons. To illustrate the dynamical characteristics of the attained solutions, the three-dimensional (3D) and contour plots of some of the representative attained solutions are displayed with the particular choice of the free parameters. The obtained solutions and their physical features might be helpful to understand the propagation of small but finite amplitude waves in shallow water.



中文翻译:

共振多条纹,复数子和团块的波传播及其对(2 + 1)维pKP方程的多种相互作用解

这项研究涉及(2 + 1)维势Kadomtsev-Petviashvili(pKP)方程,该方程用于描述物理学中不同领域和应用数学领域中二维振幅小的但有限振幅的波的动力学。通过使用Maple进行符号计算,结合Hirota的双线性方法(HBM),通过简化的线性叠加原理,得出了真实场中的共振多条纹解和复杂场中的多条纹复解。此外,通过采用HBM可以导出块状,块状条纹和块状三角形周期波解。具有指数,双曲余弦和三角余弦函数的正二次函数被认为可以达到上述目的。对于整体解决方案,发现在传播过程中,团状波的形状和幅度保持不变。另一方面,块状条纹互作用孤子呈现出块状和条纹孤子之间的裂变和融合相互作用现象。为了说明获得的解决方案的动力学特性,显示了一些代表性的获得的解决方案的三维(3D)和等高线图,其中特别选择了自由参数。所获得的解及其物理特征可能有助于理解小的但有限振幅的波在浅水中的传播。在自由参数的特定选择下,将显示某些代表性解决方案的三维(3D)和等高线图。所获得的解及其物理特征可能有助于理解小的但有限振幅的波在浅水中的传播。在自由参数的特定选择下,将显示某些代表性解决方案的三维(3D)和等高线图。所获得的解及其物理特征可能有助于理解小的但有限振幅的波在浅水中的传播。

更新日期:2021-05-04
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