29 Tachyons of Plastic Deformation
313
If we introduce another function ρ
T
= ρ
T
(x − v t) according to
ρ
T
(x − ut) =
1
c 2
o
1
κ 2
4 σa
2
L 2
o
exp
−2
π(x − ut)
L o κ
1 + exp
−2
π(x − ut)
L o κ
2
(436)
as well as a parameter o according to
o =
σ a
2
2Ł 2
o
,
(437)
we receive for the first component −t of the energy-momentum tensor
− t = u
2
ρ
T
(x − ut) .
(438)
We also find
−
σ
c 2
o
∂q
T
∂x
∂q
T
∂t
= −
1
c 2
o
(−u)
4 σa
2
L 2
o κ 2
exp
−
π(x − ut)
L o κ
1 + exp
−2
π(x − ut)
L o κ
2
and thus
p = u ρ
T
(x − ut)
(438a)
and also, according to (289),
− s = − c o u ρ
T
(x − ut) .
(438b)
Finally it follows that
−
σ
2
∂q T
∂x
∂q T
∂x
+
1
c 2
o
∂q T
∂t
∂q T
∂t
+
σa 2
4L 2
o
cos(
2π
a
q T ) − 1
= −
σ
2
4 a 2
L 2
o κ 2
1+
u 2
c 2
o
exp
−2
π(x − ut)
L o κ
1+exp
−2
π(x −ut)
L o κ
2 +
σa 2
4L 2
o
⎛
⎜
⎜
⎜
⎝
8
exp
−2
π(x − ut)
L o κ
1+exp
−2
π(x −ut)
L o κ
2 − 2
⎞
⎟
⎟
⎟
⎠