Solution 2 to problem v1l1o35

Expressions | Parameters | Relevance | Back to problem v1l1o35

Expressions

The solution is given through the following expressions:


b9=0


     5    2
    ---*a2 *b1
     6
b8=------------
         2
       a1


b7=0


b6=0


     10
    ----*a2*b1
     3
b5=------------
        a1


     5
    ---*a2*b1
     3
b4=-----------
       a1


     10
    ----*a2*b1
     3
b3=------------
        a1


     5
    ---*a2*b1
     3
b2=-----------
       a1


a3=0

Parameters

Apart from the condition that they must not vanish to give a non-trivial solution and a non-singular solution with non-vanishing denominators, the following parameters are free:

 b1,a2,a1

Relevance for the application:

The solution given above tells us that v_s is a higher order symmetry for v_t where v=v(t,x) is a vector function of arbitrary dimension and f(..,..) is the scalar product between two such vectors:

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

df(v,t)=v  *a1 + v *f(v,v)*a2
         3x       x

               2       5                         10
df(v,s)=(v  *a1 *b1 + ---*v  *f(v,v)*a1*a2*b1 + ----*v  *f(v,v )*a1*a2*b1
          5x           3   3x                    3    2x      x

             5                          10
          + ---*v *f(v ,v )*a1*a2*b1 + ----*v *f(v,v  )*a1*a2*b1
             3   x    x  x              3    x      2x

             5           2   2       2
          + ---*v *f(v,v) *a2 *b1)/a1
             6   x