n维空间中求解一类波动方程的方法

求解波动方程的初值问题一般可采用分离变量法、积分变换法、特征线法、行波法和球面平均法等方法.给出了n维空间中一类特殊波动方程求解方法.即当空间维数为奇数时,通过适当的变换,将波动方程转化为热传导方程,利用热传导方程的结果导出所求波动方程的解;当空间维数为偶数时,用降维法得到所求波动方程的解.

The solution of a special kind of wave equation in n-dimensional space

The wave equation for the initial problems generally avail of separation of variables,integral transformation,characteristics.Traveling-wave and spherical average method.Given solution of a special kind of wave equation in n-dimensional space.When the space dimension is odd,turn the wave equation into heat conduction equation through the appropriate transform.The thermal conduction equations and the results are derived for the wave equation solution.When the space dimension is even,victoria was down by the law for the wave equation solution.