Stability analysis, [Formula: see text] model expansion method, and diverse chaos-detecting tools for the DSKP model

Area of Science:

• Nonlinear Dynamics
• Mathematical Physics
• Fluid Mechanics

Background:

• The Davey-Stewartson-Kadomtsev-Petviashvili (DSKP) model is crucial for understanding shallow-water waves, coastal engineering, fluid mechanics, and plasma physics.
• Investigating nonlinear models requires robust analytical and computational methods.

Purpose of the Study:

• To apply the [Formula: see text]-model expansion method to the (4+1)-dimensional DSKP model.
• To explore novel dynamical optical solitons and analyze the model's complex behaviors.

Main Methods:

• Transformation of partial differential equations into ordinary differential equations using a variable relation.
• Application of computational software for model analysis.
• Utilizing Jacobi elliptic, hyperbolic, and trigonometric functions for solution generation.
• Employing planar dynamical analysis and chaos-identification tools.

Main Results:

• Discovery of novel dynamical optical solitons through the combination of various solution forms.
• Qualitative examination of the governing model using planar dynamical processes.
• Comprehensive investigation of stability, bifurcation, and chaotic behavior.

Conclusions:

• The [Formula: see text]-model expansion method is effective and suitable for analyzing complex nonlinear models.
• The findings provide valuable insights into the dynamics of the DSKP model and related phenomena.
• The approach offers a favorable and helpful framework for nonlinear model analysis.