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$$u_{tt}-a^2 u_{xx}=0 \hspace{1zw}(u=u(t,x),\ a\mbox{ $B$O@5$NDj?t(B})$$ (1)

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$$D_t=\frac{\partial}{\partial t},\ D_x=\frac{\partial}{\partial x}$$

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$$(D_t^2 - a^2 D_x^2)u = 0$$

$B$H=q$1!"(B$a$ $B$ODj?t$J$N$G!"HyJ,1i;;;R$KBP$7$F@.$jN)$D8x<0(B

$$D_t^2 - a^2 D_x^2 = (D_t - aD_x)(D_t + aD_x) =(D_t + aD_x)(D_t - aD_x)$$

$B$K$h$j!"(B

$$(D_t - aD_x)(D_t + aD_x) u =(D_t + aD_x)(D_t - aD_x) u = 0$$

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$$(D_t+a D_x)u=0$$ (2)

$B$^$?$O(B

$$(D_t-a D_x)u=0$$ (3)

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$$u(t,x) = f(x-at)$$ (4)

$$u(t,x) = g(x+at)$$ (5)

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$$u(t,x)=f(x-at)+g(x+at)$$ (6)

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2 $B3,$NJ}Dx<0$N2r$,!">o$K(B 1 $B3,$NJ}Dx<0$N2r$+$iF@$i$l$k$H$O8B$i$J$$$,!"(B 1 $Bl9g$O(B (1) $B$H!"(B (2) $B$d(B (3) $B$N7A$NJ}Dx<0(B

$$u_t+a u_x=0 \hspace{1zw}(\mbox{$B$^$?$O(B } u_t-a u_x =0)$$

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