中文摘要：

针对随机噪声和单频波在非线性介质中的互作用现象,本文研究其传播过程中不同频率的能量演化规律,讨论随机噪声场在加入强单频波后对其功率谱的影响规律。从Rudenko推导的噪声和单频波的非线性互作用方程出发,理论研究其中能量在不同距离的功率谱变化,并利用有限差分方法,数值求解噪声与单频波非线性互作用过程中不同距离的功率谱。给出了不同情况下强单频波对随机噪声能量在频域范围的重新分配规律,结果表明：对于高频波频率比噪声频率高的情况,噪声的能量被调制到高频及其谐波两侧;高频波频率在噪声频带内会使原噪声在频域展宽;有限振幅噪声能量的转换效率在加入高频波情况下将会提高。

英文摘要：

Focusing on the interaction between random noise and single-frequency waves in a nonlinear medium, this study investigated the energy evolution law that governs the propagation of different frequencies. The effect of the random noise field on its power spectrum after the addition of the strong single-frequency wave is also discussed. The change in the energy power spectrum at different distances is investigated on the basis of the nonlinear interactive equation of noise and single-frequency wave deduced by Rudenko. In addition, the power spectrum at different distances in the nonlinear interaction between noise and single-frequency wave is numerically solved through the finite difference method. The redistribution law of strong single-frequency wave against random noise energy in the frequency scope under different situations is also provided. When the frequency of the high-frequency wave is higher than that of noise frequency, the noise energy is modulated to both sides of the high frequency and its harmonic wave. The frequency of the high-frequency wave extends the original noise within the noise freque efficiency of the noise energy in the finite amplitude will increase after the addition of ncy band. The transformation the high-frequency wave.