Abstract: This paper considers the exact solutions of a (2+1)-dimensional nonlinear partial differential equation composed of the KP equation, the Ito equation, and the shallow water wave equation. Firstly, by performing a variable transformation on the unknown function and taking appropriate integration constants, the Hirota bilinear form of the equation is obtained. Secondly, by using the homoclinic test method with the auxiliary function set as an exponential function and a trigonometric function, the soliton solutions and breather solutions of the equation are presented and the dynamic properties of the solutions are demonstrated. Subsequently, by employing the positive quadratic function method with the auxiliary function set as a polynomial type function, four sets of lump solutions of the equation are constructed and the properties of the solutions such as amplitude and wave velocity are analyzed. Finally, through the extended positive quadratic function method, the interaction solutions of the equation expressed by exponential functions and polynomial functions, including lump-stripe soliton solutions, are obtained, and the phenomenon of solution swallowing is displayed.