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Abundant Bounded and Unbounded Solitary, Periodic, Rogue‐Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model

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  • Mohammad Mobarak Hossain
  • Alrazi Abdeljabbar
  • Harun-Or Roshid
  • Md. Mamunur Roshid
  • Abu Naim Sheikh

Abstract

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon (KG) model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation (MSE) technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of all phase portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue‐type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue‐type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics.

Suggested Citation

  • Mohammad Mobarak Hossain & Alrazi Abdeljabbar & Harun-Or Roshid & Md. Mamunur Roshid & Abu Naim Sheikh, 2022. "Abundant Bounded and Unbounded Solitary, Periodic, Rogue‐Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:8771583
    DOI: 10.1155/2022/8771583
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    1. Wei-Guo Zhang & Xing-Qian Ling & Xiang Li & Shao-Wei Li, 2019. "The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms," Complexity, Hindawi, vol. 2019, pages 1-17, June.
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