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.