Dynamics of three-wave solitons and other localized wave solutions to a new generalized (3+1)-dimensional P-type equation

This study investigates the nonlinear wave equation in soliton theory, specifically focusing on the new generalized (3+1)-dimensional P-type equation. By employing the Hirota bilinear method, we successfully derive the dynamics of multiwave solutions with trigonometric and hyperbolic functions such as one-soliton, two-soliton, three-soliton, Kuznetsov–Ma breather soliton, Homoclinic breather soliton, M-shaped soliton and W-shaped soliton. To visually represent the obtained solutions, we depict them through 2D and 3D plots, showcasing various dynamical structures along with diverse sets of parameters for a more comprehensive physical understanding. Additionally, we conduct a stability analysis of the governing equation, offering stability criteria along with the corresponding regions of stability. The outcomes are novel, valuable, and represent unexplored territory for the examined equation, as no prior studies have delved into these findings.