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Solitary travelling wave profiles to the nonlinear generalized Calogero–Bogoyavlenskii–Schiff equation and dynamical assessment

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Abstract

This study focuses on the nonlinear generalized Calogero–Bogoyavlenskii–Schiff equation to explain the wave profiles in soliton theory. The improved and efficient technique is applied to derive soliton solutions that are dependent, significant, and more broadly applicable for this equation, surpassing the intricacy of prior complex travel equations. The generalized projective Riccati equations method is employed to acquire precise travelling wave solutions, encompassing various types such as U-shaped, bright, bell-shaped, dark, and flat kink-type wave peakon solutions. These soliton solutions are represented using trigonometric and hyperbolic functions. The graphical presentation of the travelling wave pattern solutions of the model is achieved through the use of the Wolfram Mathematica software for the visualization of the impact of the involved parameters. 3D, contour, and 2D surfaces depict the propagating behaviours of the obtained solutions. Sensitivity analysis is conducted to observe the dynamics of the model, particularly the wave velocity parameter controls the water waves. Furthermore, quasi-periodic chaotic, quasi-periodic, and periodic systems are investigated to understand the model’s dynamics further. The analysis demonstrates the reliability and efficiency of the employed technique, making it applicable for finding suitable solitary travelling wave solutions for a wide range of nonlinear evolution equations.

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No data sets were collected or analysed during this study; there is no applicable data sharing for this paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, Pakistan

    Sheikh Zain Majid, Muhammad Imran Asjad & Waqas Ali Faridi

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  1. Sheikh Zain Majid
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  2. Muhammad Imran Asjad
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Contributions

SZM and MIA contributed to the problem formulation and formal analysis. MIA and WAF were involved in the investigation and methodology. SZM and MIA provided supervision and resources. MIA and WAF conducted the validation, software development, and graphical discussions. SZM and MIA also contributed to the editing and review of the manuscript. All authors participated in editing and reviewing the manuscript and have approved the final version for submission.

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Correspondence to Sheikh Zain Majid.

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Majid, S.Z., Asjad, M.I. & Faridi, W.A. Solitary travelling wave profiles to the nonlinear generalized Calogero–Bogoyavlenskii–Schiff equation and dynamical assessment. Eur. Phys. J. Plus 138, 1040 (2023). https://doi.org/10.1140/epjp/s13360-023-04681-z

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