Exploring nonlinear wave dynamics and stability in the Jaulent–Miodek equation: an extended direct algebraic method with LM-ANN

Key Points

• Nonlinear wave dynamics and stability in the Jaulent–Miodek equation are examined using a novel approach.
• The analysis identifies key patterns, enhancing understanding of complex systems and predicting behaviors.
• An extended direct algebraic method combined with LM-ANN facilitates deeper insights into wave behavior.
• These findings contribute to advanced mathematical modeling, supporting further research in nonlinear dynamics.