Traditional research methods for addressing nonlinear problems in radio frequency (RF) amplifiers often suffer from complexity, high computational demands, and limited precision. To overcome these challenges, this paper proposes a nonlinear modeling approach using neural networks. The fundamental principles and mechanisms of neural networks are introduced, highlighting their advantages in nonlinear modeling and analysis. The nonlinear characteristics of RF power amplifiers in satellite communications, including nonlinear distortion and nonlinear gain, are thoroughly examined. By collecting extensive input and output data from RF power amplifiers, a neural network model is constructed, trained, and optimized. Experimental results demonstrate that applying neural networks to analyze the nonlinear characteristics of RF power amplifiers in satellite communications significantly improves analysis precision (maximum: 97.9%), reduces computational complexity (minimum: 0.209), and enables comprehensive nonlinear analysis. This approach is of great significance for optimizing the performance and reliability of satellite communication systems.