A dynamical behavior of the coupled Broer-Kaup-Kupershmidt equation using two efficient analytical techniques

Area of Science:

• Nonlinear Dynamics
• Mathematical Physics
• Wave Phenomena

Background:

• The coupled Broer-Kaup-Kupershmidt (BKK) system models complex nonlinear wave evolution in diverse fields like fluid dynamics, plasma physics, and optics.
• Understanding these nonlinear waves is crucial for applications involving dispersive and long-gravity waves.

Purpose of the Study:

• To investigate and identify multiple soliton solutions for the nonlinear coupled BKK system.
• To explore the impact of different derivative types (beta, conformable, local-fractional, M-truncated) on these solutions.
• To analyze the characteristics and geometrical forms of the obtained wave solutions.

Main Methods:

• The Unified and generalised Bernoulli sub-ordinary differential equation (sub-ODE) techniques were employed to find travelling wave solutions.
• Mathematica 10 was utilized for generating 2D line graphs, contour plots, and 3D graphics to visualize and compare solutions.
• Parameter variations were used to generate a spectrum of soliton types.

Main Results:

• Multiple soliton solutions were successfully identified for the BKK system under various derivative definitions.
• Diverse wave structures were generated, including bright solitons, squeezed bell-shaped waves, singular solitons, and periodic solutions.
• A comparative analysis using graphical representations demonstrated the effectiveness of the different derivative types.

Conclusions:

• The study successfully demonstrates the application of Unified and generalised Bernoulli sub-ODE methods for solving the BKK system with various derivatives.
• The obtained solutions exhibit rich nonlinear wave behaviors and symmetrical geometrical forms, highlighting the versatility of the BKK model.
• The findings provide valuable insights into nonlinear wave dynamics and their mathematical modeling across different scientific disciplines.