<p>This paper discusses a two-layered generalized nonlinear Schrödinger (NLS) equation with third-order dispersion and extra nonlinear terms which can describe the propagation of oceanic internal solitary waves. Various novel analytical solutions for this equation are derived corresponding to different cases of a polynomial discriminant based on weak coefficient constraints, including hyperbolic function, triangular function and Jacobi elliptic function solutions. Choosing three areas in the South China Sea, the propagation characteristics of internal solitary waves have been obtained using the analytical results under environmental parameters specific to the area. The effects of nonlinear and dispersion terms, noise disturbances and water depth on the propagation and evolution of internal solitary waves in the South China Sea have been discussed numerically with the analytical solution as initial conditions. The results indicate that in complex marine environments, phenomena such as frequency shifts, width increases, and amplitude decays occur during the propagation of internal solitary waves. It can be hoped that the results obtained in this paper will provide theoretical basis for the use of generalized NLS equation for other sea areas.</p>