中文摘要：

波动理论一直是地震学的核心内容，非线性波在介质中是真实存在的，能够充分认识非线性波，将对波动理论的发展和进一步应用提供很大的帮助．本文从固体介质中的位移、应力、应变的基本关系出发，推导了非线性P波在二维固体中的传播的非线性方程，对此非线性方程，采用四阶差分的方法，研究其在二维空间中的传播特点，对非线性波的传播有了更深的认识和理解．

英文摘要：

Wave theory is the kernel content of seismology,and the nonlinear wave indeed exists in the solid,which will be helpful for the development of the wave theory and the further application if we can completely recognise it. This paper deductes the nonlinear P-wave equation in the 2-D solid based on the basic relation of the displacement, stress and strain. To this equation, using the 4 order difference method, we study the propagation characters and obtain further cognition and comprehension of the nonlinear P-wave in solid.