Numerical Solution of Modified Cubic-Boussinesq Equation using He-Kamal Transform with Lagrange Multiplier

Cubic-Boussinesq equation is very crucial for modeling nonlinear wave phenomena, capturing intricate dynamics like wave breaking and soliton interactions. Its significance lies in its ability to describe the behavior of waves in diverse physical contexts, from fluid dynamics to optical fibers. Due to the nonlinearity in the equation, finding accurate and efficient solutions might be quite challenging. This study introduces an innovative approach using the He-Kamal transform method and a Lagrange multiplier to solve the equation. The He-Kamal transform simplifies the PDE, making it more tractable, while the Lagrange multiplier enhances solution accuracy and convergence. Numerical simulations show that the He-Kamal transform with a Lagrange multiplier corresponds with traditional methods in handling the cubic nonlinearity of the Cubic-Boussinesq equation. MATLAB-generated diagrams demonstrate the effectiveness of the method in capturing wave dynamics and stability. This research advances numerical techniques for solving nonlinear PDEs and contributes to the field of nonlinear wave theory.