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n+1 |
| t Î (- ¥ , + ¥) ; (x,t) Î E |
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| We
have a new system of n equations
with n+1 unknowns. Obviously,
equation (2) describes a |
| certain curve in
space with n+1 dimensions. |
a Î (- ¥ , + ¥) ; t = t(a) ; x1 = x1(a) ; ... xn =
xn(a) .
By deriving (2) we obtain
| ì |
|
df1 |
dx1 |
+ |
df1 |
dx2 |
+ |
... |
+ |
df1 |
dxn |
- |
f01 |
dt |
= |
0; |
|
| ï |
|
dx1 |
da |
|
dx2 |
da |
|
|
|
dxn |
da |
|
|
da |
|
|
|
| ï |
|
... |
|
| ï |
|
dfn |
dx1 |
+ |
dfn |
dx2 |
+ |
... |
+ |
dfn |
dxn |
- |
f0n |
dt |
= |
0; |
|
| í |
|
dx1 |
da |
|
dx2 |
da |
|
|
|
dxn |
da |
|
|
da |
|
|
(3) |
| ï |
|
x1(
0 ) = x01; |
| ï |
|
... |
|
| ï |
|
xn(
0 )= x0n; |
| î |
|
t ( 0 ) =1 ; |
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