Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the (2+1)-dimensional KP-BBM equation
Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the (2+1)-dimensional KP-BBM equation
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DOI：
10.1007/s12043-020-02057-x
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发表时间：
2021-02-13
影响因子：
2.8
通讯作者：
Kharbanda, Harsha
中科院分区：
文献类型：
--
作者：
Kumar, Sachin;Kumar, Dharmendra;Kharbanda, Harsha
本文的主要目的是利用两种强有力的技巧，Lie对称方法和广义指数有理函数（GERF）方法，借助Mathematica的符号计算，构造（2+1）维Kadomtsev-Petviashvili-Benjamin-Bona-Mahony（KP-BBM）方程的丰富的精确解.首先，我们导出了无穷小量、几何向量场、对易关系和最优系统。因此，KP-BBM方程在两个阶段的对称性约化下被约化为多个非线性常微分方程。此外，还得到了不同形状的单孤子、孤波解、准周期波孤子、弹性多孤子、暗孤子和亮孤子等丰富的解，由于自由参数和常数的存在，这些解对描述物理现象更有意义和实用性.所有这些精确孤子解都是新的，与以前的研究结果完全不同。此外，还利用数学软件对所得到的精确封闭解的动力学行为进行了三维、二维波形图和相应的密度图的图形分析，这将被广泛地用于解释非线性物理、等离子体物理、光学物理、数学物理、非线性动力学等领域中的复杂物理现象。
In the present article, our main aim is to construct abundant exact solutions for the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation by using two powerful techniques, the Lie symmetry method and the generalised exponential rational function (GERF) method with the help of symbolic computations via Mathematica. Firstly, we have derived infinitesimals, geometric vector fields, commutation relations and optimal system. Therefore, the KP-BBM equation is reduced into several nonlinear ODEs under two stages of symmetry reductions. Furthermore, abundant solutions are obtained in different shapes of single solitons, solitary wave solutions, quasiperiodic wave solitons, elastic multisolitons, dark solitons and bright solitons, which are more relevant, meaningful and useful to describe physical phenomena due to the existence of free parameters and constants. All these generated exact soliton solutions are new and completely different from the previous findings. Moreover, the dynamical behaviour of the obtained exact closed-form solutions is analysed graphically by their 3D, 2D-wave profiles and the corresponding density plots by using the mathematical software, which will be comprehensively used to explain complex physical phenomena in the fields of nonlinear physics, plasma physics, optical physics, mathematical physics, nonlinear dynamics, etc.