Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation,Journal of Advanced Research

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Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation
Journal of Advanced Research ( IF 11.4 ) Pub Date : 2021-10-13 , DOI: 10.1016/j.jare.2021.09.015
Mingchen Zhang ₁ , Xing Xie ₂ , Jalil Manafian _{3,

4} , Onur Alp Ilhan ₅ , Gurpreet Singh ₆

Affiliation

Introduction

The multiple Exp-function scheme is employed for searching the multiple soliton solutions for the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation.

Objectives

Moreover, the Hirota bilinear technique is utilized to detecting the lump and interaction with two stripe soliton solutions.

Methods

The multiple Exp-function scheme and also, the semi-inverse variational principle will be used for the considered equation.

Results

We have obtained more than twelve sets of solutions including a combination of two positive functions as polynomial and two exponential functions. The graphs for various fractional-order $α$ are designed to contain three dimensional, density, and y-curves plots. Then, the classes of rogue waves-type solutions to the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation within the frame of the bilinear equation, is found.

Conclusion

Finally, a direct method which is called the semi-inverse variational principle method was used to obtain solitary waves of this considered model. These results can help us better understand interesting physical phenomena and mechanism. The dynamical structures of these gained lump and its interaction soliton solutions are analyzed and indicated in graphs by choosing suitable amounts. The existence conditions are employed to discuss the available got solutions.

中文翻译：

分数阶广义CBS-BK方程的新多重流氓波解的特征

介绍

多重 Exp 函数方案用于搜索分数广义 Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko 方程的多个孤子解。

目标

此外，Hirota 双线性技术用于检测块和与两个条纹孤子解的相互作用。

方法

多重 Exp 函数方案以及半逆变分原理将用于所考虑的方程。

结果

我们已经获得了超过十二组的解决方案，包括两个正函数的组合作为多项式和两个指数函数。各种分数阶的图表 $α$ 被设计成包含三维、密度和y曲线图。然后，在双线性方程的框架内，找到分数广义Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko方程的流氓波型解的类别。