Constructing new high-dimensional nonlinear evolution equations and deriving new nonlinear wave solutions have always been open problems in mathematical physics and engineering. In this paper, we extend a completely integrable \((3+1)\) -dimensional Kadomtsev-Petviashvili equation to a more general version, which is a special reduction of (4+2)-dimensional Kadomtsev-Petviashvili equation. The Wronskian and Grammian determinant solutions of the \((3+1)\) -dimensional Kadomtsev-Petviashvili equation are first derived. Then, a range of ripple wave solutions involving Airy functions are obtained. The \((3+1)\) -dimensional Kadomtsev-Petviashvili I equation acknowledges the parabolic ripple solitons with an opening in the positive x-axis direction and line ripple solitons. However, the \((3+1)\) -dimensional Kadomtsev-Petviashvili II equation admits the parabolic ripple solitons with an opening in the negative x-axis direction and line rogue solitons. These solutions describe a series of oscillating curve solitons that dissipate with time and eventually approach a constant background plane as time approaches infinity. The evolution of these solutions is more closely matched with the dynamics of water waves in nature, and has more practical significance. Additionally, we also discussed these new solutions from both analytical and numerical perspectives, and these results will provide reference for discovering new nonlinear waves.
