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Soliton’s behavior and stability analysis to a model in mathematical physics

Author

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  • Islam, Md. Ekramul
  • Mannaf, Md. Abde
  • Khan, Kamruzzaman
  • Akbar, M. Ali

Abstract

The Hamiltonian amplitude model is one of the important ways to describe Hamiltonian mechanics. This study aims to investigate the model to discover the mechanisms of the obtained solutions through two analytical schemes and interpret the stability of the solitons at several equilibrium points via bifurcation analysis along with the Hamiltonian system. Additionally, we find out the crucial point of the particles in nature consisting of the stated model. Furthermore, we demonstrate the equilibrium point in the graphical representation to analyze the stability of the signal by describing the saddle point and center of the system. Thus the novelty of this investigation is that the attained solutions of the stated model deliver several types of waves such as periodic, lump, rogue, breather, dark, and bright soliton depending on time and wave displacement parameters that are depicted in 3D and 2D figures. We also analyze the nature of the wave based on two diffusion constants of the governing model and describe the effect of these parameters on the wave profile. As can stated the bifurcation analysis and the two implemented methods are very useful and informative to describe the mathematical model in future studies like this investigation and many more.

Suggested Citation

  • Islam, Md. Ekramul & Mannaf, Md. Abde & Khan, Kamruzzaman & Akbar, M. Ali, 2024. "Soliton’s behavior and stability analysis to a model in mathematical physics," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005162
    DOI: 10.1016/j.chaos.2024.114964
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    References listed on IDEAS

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    1. Sheu, Long-Jye & Tam, Lap-Mou & Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaotic convection of viscoelastic fluids in porous media," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 113-124.
    2. Dubey, Shweta & Chakraverty, S., 2022. "Application of modified extended tanh method in solving fractional order coupled wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 509-520.
    3. Wang, Mingliang & Li, Xiangzheng, 2005. "Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1257-1268.
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