Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation

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 $\alpha$ 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.