Home ] Up ] Page 3 ]

                       

F(x) – t * F0 = 0 ;  (2)
n+1
t Î (- ¥ , + ¥) ; (x,t) Î
    
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 ;