有界空间中的非线性声学和收敛的积累解

在微扰近似下,拉格朗日体系下的一阶、二阶波动方程解是具势运动,应用拉格朗日变动参数法来寻求积累解。在一般情况下,二阶波的波动方程在半空间会出现各式各样的积累解,它们沿着3个坐标变量的方向都有积累,在理想介质中它们不满足辐射条件。本文的结果表明,在考虑到介质的非理想性之后,也只有沿着平面边界面法线方向有积累的积累解才满足辐射条件,因而是收敛的。 

Nonlinear acoustics in bounded space and accumulating solutions of convergence

Under the perturbation approximation, the solutions of the first- and second- order wave equations in the Lagrange system are potential motion. The accumulating solutions of the relevant wave equations were obtained by mean of the Lagrange variable parameter method. In general, the wave equation of the two order wave will have various accumulation solutions in the half space. They will accumulate along the direction of the three coordinate variables, and they will not satisfy the radiation condition in the ideal medium. The results of this paper show that after considering the non- ideality of the medium, only the accumulated solution along the normal direction of the plane boundary satisfies the radiation condition, so it is convergent.