3. The third point is related to the first one. In (3), the transport equation was applied to the waves in *unbounded* media; the energy components $W+(x,k,t)$ and $W\u2212(x,\u2212k,t)$ correspond to two simple eigenvalues $\xb1\omega $, so that $W+(x,k,t)=W\u2212(x,\u2212k,t)$. In fact, they are the same quantities but in inverse direction to infinity $(\xb1\u221e)$, and they cannot be superposed. Thus,Display Formula

$W(x,t)=\u222bR3W+(x,k,t)dk,I(x,t)=c(x)\u222bR3W+(x,k,t)k\u0302dk$

(1)

In the paper,

$W+$ and

$W\u2212$ represent the progressive and regressive wave energies propagating in

*bounded* media. Especially in damped cases,

$W+\u2260W\u2212$. By the principle of superposition under some assumptions, the energy density and power flow density could be written as

Display Formula$W(x,t)=\u222bR3[W+(x,k,t)+W\u2212(x,\u2212k,t)]dk$

(2)

Display Formula$I(x,t)=c(x)\u222bR3[W+(x,k,t)\u2212W\u2212(x,\u2212k,t)]k\u0302dk$

(3)