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<p>This study investigates solitary wave solutions, chaotic behaviors, bifurcation analysis, sensitivity, and stability of the stochastic Davey-Stewartson equations. Using the extended modified auxiliary equation mapping method (EMAEMM), novel analytical traveling wave solutions, including single, dark, and bright singular solitons, are derived. The Galilean transformation converts the system into a planar dynamical framework, enabling analysis of sensitivity, chaos, and bifurcations through Lyapunov exponents, Poincaré maps, phase diagrams, and time series plots. A positive Lyapunov exponent confirms chaotic behavior, illustrated with visual and tabular results. Stability of the solutions is validated via Hamiltonian analysis. This work underscores the effectiveness of EMAEMM and suggests avenues for extending soliton dynamics research to broader scenarios.</p>

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Stability, sensitivity, chaotic behavior, and phase trajectories evaluation of the Davey-Stewartson stochastic equation

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Nadia Cheemaa,
  • H. M. A. Siddiqui,
  • Bismah Nazir,
  • Ahmet Bekir,
  • Abdulrahman A. Almehizia,
  • Hisham H. Hussein

摘要

This study investigates solitary wave solutions, chaotic behaviors, bifurcation analysis, sensitivity, and stability of the stochastic Davey-Stewartson equations. Using the extended modified auxiliary equation mapping method (EMAEMM), novel analytical traveling wave solutions, including single, dark, and bright singular solitons, are derived. The Galilean transformation converts the system into a planar dynamical framework, enabling analysis of sensitivity, chaos, and bifurcations through Lyapunov exponents, Poincaré maps, phase diagrams, and time series plots. A positive Lyapunov exponent confirms chaotic behavior, illustrated with visual and tabular results. Stability of the solutions is validated via Hamiltonian analysis. This work underscores the effectiveness of EMAEMM and suggests avenues for extending soliton dynamics research to broader scenarios.