A novel investigation of the extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation: analysis and simulations

This study explores the extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation, which has numerous applications in plasma physics and nonlinear optics. First, by employing the Hirota bilinear method, we construct the resonant solitons, such as resonant X and \(Y-\)type solitons and hybrid solutions. Second, we generate the lump-periodic solution and lump-stripe soliton solution via ansatz wave function method. To extend this, we extract the nonlinear localized waves, such as two strip-solitons and periodic breather solutions, from the two-soliton wave. These include two cross-strip solitons, two parallel-strip solitons, \(x\)-periodic breather and \((x,y)\)-periodic breather solutions. For the validity of obtained solutions, we present them through 3D, contour and density plots using suitable freely chosen parameters, which highlight their complex structure and dynamics. At the end, we conduct stability analysis to provide a general criteria for stable and unstable steady-state solution. Our results are new and have not been previously reported for governing equation. This equation has not been extensively studied, presenting a notable research gap and the potential to significantly advance the broader understanding of nonlinear wave equations arising in surface water waves, plasma physics and nonlinear optics.