Neural-network symbolic computation for Kadomtsev–Petviashvili II equation: From classical solutions to new exact solutions with quadratic temporal dependence

Internal solitary waves in stratified shelf waters exhibit two-dimensional nonlinear evolution. Existing exact solutions of related models mainly describe constant-speed propagation and cannot fully capture time-dependent wave dynamics. In this study, the neural-network symbolic computation approach (NNSCA) is applied to the Kadomtsev–Petviashvili II (KP-II) equation. The method reproduces classical constant-speed solutions and obtains several families of analytical solutions with quadratic temporal dependence characteristics. These solutions include quadratic temporal terms ( t 2 ), which lead to non-uniform temporal evolution of the wave profiles. The obtained solutions consist of localized wave packets with time-dependent phase, algebraic deformation structures, and composite tanh 2 -type solutions. They provide additional analytical cases for the KP-II equation and can be used to test numerical algorithms and machine-learning methods for nonlinear wave equations. The solutions also provide a basis for studying the physical effects of time-dependent wave evolution. A qualitative Morison-type load analysis indicates that time-dependent phase evolution changes the temporal variation of hydrodynamic forces acting on offshore structures.