Solution 2 to problem v1l1o57
Expressions |
Parameters |
Relevance |
Back to problem v1l1o57
Expressions
The solution is given through the following expressions:
b24=0
7 3
----*a2 *b1
50
b23=-------------
3
a1
b22=0
b21=0
b20=0
b19=0
14 2
----*a2 *b1
5
b18=-------------
2
a1
14 2
----*a2 *b1
5
b17=-------------
2
a1
7 2
---*a2 *b1
5
b16=------------
2
a1
14 2
----*a2 *b1
5
b15=-------------
2
a1
7 2
----*a2 *b1
10
b14=-------------
2
a1
b13=0
b12=0
b11=0
14
----*a2*b1
5
b10=------------
a1
28
----*a2*b1
5
b9=------------
a1
21
----*a2*b1
5
b8=------------
a1
28
----*a2*b1
5
b7=------------
a1
14*a2*b1
b6=----------
a1
42
----*a2*b1
5
b5=------------
a1
7*a2*b1
b4=---------
a1
28
----*a2*b1
5
b3=------------
a1
7
---*a2*b1
5
b2=-----------
a1
a9=0
3 2
----*a2
10
a8=----------
a1
a7=0
a6=0
a5=2*a2
a4=a2
a3=2*a2
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:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2
df(v,t)=(v *a1 + v *f(v,v)*a1*a2 + 2*v *f(v,v )*a1*a2 + v *f(v ,v )*a1*a2
5x 3x 2x x x x x
3 2 2
+ 2*v *f(v,v )*a1*a2 + ----*v *f(v,v) *a2 )/a1
x 2x 10 x
3 7 2 28 2
df(v,s)=(v *a1 *b1 + ---*v *f(v,v)*a1 *a2*b1 + ----*v *f(v,v )*a1 *a2*b1
7x 5 5x 5 4x x
2 42 2
+ 7*v *f(v ,v )*a1 *a2*b1 + ----*v *f(v,v )*a1 *a2*b1
3x x x 5 3x 2x
7 2 2 2
+ ----*v *f(v,v) *a1*a2 *b1 + 14*v *f(v ,v )*a1 *a2*b1
10 3x 2x x 2x
28 2 14 2
+ ----*v *f(v,v )*a1 *a2*b1 + ----*v *f(v,v )*f(v,v)*a1*a2 *b1
5 2x 3x 5 2x x
21 2 28 2
+ ----*v *f(v ,v )*a1 *a2*b1 + ----*v *f(v ,v )*a1 *a2*b1
5 x 2x 2x 5 x x 3x
7 2 14 2
+ ---*v *f(v ,v )*f(v,v)*a1*a2 *b1 + ----*v *f(v,v )*a1 *a2*b1
5 x x x 5 x 4x
14 2 14 2 2
+ ----*v *f(v,v )*f(v,v)*a1*a2 *b1 + ----*v *f(v,v ) *a1*a2 *b1
5 x 2x 5 x x
7 3 3 3
+ ----*v *f(v,v) *a2 *b1)/a1
50 x