Cross-kink wave, solitary, dark, and periodic wave solutions by bilinear and He’s variational direct methods for the KP–BBM equation
Cross-kink wave, solitary, dark, and periodic wave solutions by bilinear and He’s variational direct methods for the KP–BBM equation
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KP-BBM 方程的双线性和 He 变分直接法的交扭波、孤立波、暗波和周期波解
DOI：
10.1142/s0217979221502751
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发表时间：
2021
影响因子：
1.7
通讯作者：
A. H. Agadi
中科院分区：
文献类型：
--
作者：
Baolin Feng;J. Manafian;O. Ilhan;A. Rao;A. H. Agadi
本文研究了不可压缩流体中（2+1）维KP-BBM方程的交叉扭结波。基于Hirota的双线性技巧，构造了KP-BBM方程的交叉扭折解。采用特殊约化，得到了包括指数函数、三角函数和双曲函数在内的不同类型解的精确表达式。利用基于变分理论的He变分直接方法和Ritz类方法构造了（2+1）维广义Hirota-Satsuma-Ito方程的丰富行波解.这些行波解包括弯曲暗孤波解、暗孤波解、亮孤波解、周期波解等，它们都依赖于Ritz类方法的初始假设。在此基础上，利用调制不稳定性讨论了所得解的稳定性。此外，还研究了广义Hirota-Satsuma-Ito方程的有理[公式：见正文]方法.所获得的解决方案的适用性和有效性，通过三维和二维图形的形式的数值结果。各种相互作用的分析和图形说明。分析和总结了参数对传播的影响。所得结果和现象丰富了非线性波演化的动力学行为。
This paper deals with cross-kink waves in the (2+1)-dimensional KP–BBM equation in the incompressible fluid. Based on Hirota’s bilinear technique, cross-kink solutions related to KP–BBM equation are constructed. Taking the special reduction, the exact expression of different types of solutions comprising exponential, trigonometric and hyperbolic functions is obtained. Moreover, He’s variational direct method (HVDM) based on the variational theory and Ritz-like method is employed to construct the abundant traveling wave solutions of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation. These traveling wave solutions include kinky dark solitary wave solution, dark solitary wave solution, bright solitary wave solution, periodic wave solution and so on, which are all depending on the initial hypothesis for the Ritz-like method. In continuation, the modulation instability is engaged to discuss the stability of the obtained solutions. Moreover, the rational [Formula: see text] method on the generalized Hirota–Satsuma–Ito equation is investigated. The applicability and effectiveness of the acquired solutions are presented through the numerical results in the form of 3D and 2D graphs. A variety of interactions are illustrated analytically and graphically. The influence of parameters on propagation is analyzed and summarized. The results and phenomena obtained in this paper enrich the dynamic behavior of the evolution of nonlinear waves.