一维非线性脉冲波的两波干扰

Two-Wave Interference for One-Dimensional Nonlinear Pulse Waves

讨论在一维情形下初值具有脉冲形式的常系数半线性偏微分方程的Cauchy问题。利用渐近分析的方法,求出反映两脉冲波干扰的近似解的表达式,通过近似解与精确解的误差分析(扰动方法),得出近似解是精确解的一个好的近似。

In one dimension case, a Cauchy problem with pulse like initial data for a semilinear strict hyperholic equations with constant coefficients is discussed. With the aid of asymptotic analysis method, the approximate solution to reflect the interaction of two pulse waves is derived. By analysing the error between the exact solution and the approximate solution, the conclusion obtained is that the approximate solution is a good approximation of the exact solution.