Nonlinear dispersion relations of wave

Based on the summarization and comparison of present nonlinear dispersion relations of wave,the general expression of the nonlinear dispersion relations and its explicit form are presented in this paper. The result of comparison shows that the explicit form has a considerably high precision and is good agreement with the implicit form. By use of the explicit form of nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinear term,a mathematical model of wave transformation considering the effect of the nonlinearity is obtained. Comparison of the modified nonlinear relations is made in the model,and the computed results show that it is more accurate to use the latest nonlinear relation.