Abstract: In the medical diagnosis and treatment and the nondestructive inspection of micro or mesoscopic injury it is often necessary to characterize the material nonlinear coefficients of the medium to obtain more accurate change of mechanical properties in local areas. Based on the brief description of nonlinear acoustic equations in isotropic solid and ideal fluid, it can be found that the three equations have similar forms, and it means that the solutions of the three equations have similar forms and propagation characteristics. Then, five methods, including finite difference method (FDTD), finite element method, perturbation method (PERT), Pseudo linear solution (PSEU), and tradition solution, are employed to solve the one-dimensional nonlinear acoustic equation. Through comparing these solutions with experimental results, it is shown that several theoretical solutions of second harmonic propagation characteristics can meet the experimental results well; and, the time domain waveforms calculated by using some method can display the evolutionary process from sinusoidal to shock wave. Finally, the advantages and disadvantages of these solutions are compared and discussed. The higher order perturbation solution can provide broader experimental conditions and better technical methods for measuring the nonlinear coefficients of medium. The comparison of several solutions of the nonlinear acoustic equation also improves the theoretical study of nonlinear acoustics.