Solution 1 to problem v1l1o57
Expressions |
Parameters |
Relevance |
Back to problem v1l1o57
Expressions
The solution is given through the following expressions:
21 3
----*a2 *b1
25
b24=-------------
3
a1
7 3
----*a2 *b1
25
b23=-------------
3
a1
189 2
-----*a2 *b1
25
b22=--------------
2
a1
49 2
----*a2 *b1
25
b21=-------------
2
a1
147 2
-----*a2 *b1
25
b20=--------------
2
a1
21 2
----*a2 *b1
5
b19=-------------
2
a1
2
7*a2 *b1
b18=----------
2
a1
28 2
----*a2 *b1
5
b17=-------------
2
a1
98 2
----*a2 *b1
25
b16=-------------
2
a1
126 2
-----*a2 *b1
25
b15=--------------
2
a1
21 2
----*a2 *b1
25
b14=-------------
2
a1
7
---*a2*b1
5
b13=-----------
a1
21
----*a2*b1
5
b12=------------
a1
7*a2*b1
b11=---------
a1
28
----*a2*b1
5
b10=------------
a1
77
----*a2*b1
5
b9=------------
a1
56
----*a2*b1
5
b8=------------
a1
49
----*a2*b1
5
b7=------------
a1
126
-----*a2*b1
5
b6=-------------
a1
56
----*a2*b1
5
b5=------------
a1
49
----*a2*b1
5
b4=------------
a1
7*a2*b1
b3=---------
a1
7
---*a2*b1
5
b2=-----------
a1
4 2
---*a2
5
a9=---------
a1
2 2
---*a2
5
a8=---------
a1
a7=a2
a6=2*a2
a5=3*a2
a4=2*a2
a3=3*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 + 3*v *f(v,v )*a1*a2 + 2*v *f(v ,v )*a1*a2
5x 3x 2x x x x x
2 2 2
+ 3*v *f(v,v )*a1*a2 + ---*v *f(v,v) *a2 + 2*f(v ,v )*a1*a2*v
x 2x 5 x x 2x
4 2
+ f(v,v )*a1*a2*v + ---*f(v,v )*f(v,v)*a2 *v)/a1
3x 5 x
3 7 2 2
df(v,s)=(v *a1 *b1 + ---*v *f(v,v)*a1 *a2*b1 + 7*v *f(v,v )*a1 *a2*b1
7x 5 5x 4x x
49 2 56 2
+ ----*v *f(v ,v )*a1 *a2*b1 + ----*v *f(v,v )*a1 *a2*b1
5 3x x x 5 3x 2x
21 2 2 126 2
+ ----*v *f(v,v) *a1*a2 *b1 + -----*v *f(v ,v )*a1 *a2*b1
25 3x 5 2x x 2x
49 2 126 2
+ ----*v *f(v,v )*a1 *a2*b1 + -----*v *f(v,v )*f(v,v)*a1*a2 *b1
5 2x 3x 25 2x x
56 2 77 2
+ ----*v *f(v ,v )*a1 *a2*b1 + ----*v *f(v ,v )*a1 *a2*b1
5 x 2x 2x 5 x x 3x
98 2 28 2
+ ----*v *f(v ,v )*f(v,v)*a1*a2 *b1 + ----*v *f(v,v )*a1 *a2*b1
25 x x x 5 x 4x
28 2 2 2
+ ----*v *f(v,v )*f(v,v)*a1*a2 *b1 + 7*v *f(v,v ) *a1*a2 *b1
5 x 2x x x
7 3 3 2
+ ----*v *f(v,v) *a2 *b1 + 7*f(v ,v )*a1 *a2*b1*v
25 x 2x 3x
21 2 21 2
+ ----*f(v ,v )*a1 *a2*b1*v + ----*f(v ,v )*f(v,v)*a1*a2 *b1*v
5 x 4x 5 x 2x
147 2 7 2
+ -----*f(v ,v )*f(v,v )*a1*a2 *b1*v + ---*f(v,v )*a1 *a2*b1*v
25 x x x 5 5x
49 2
+ ----*f(v,v )*f(v,v)*a1*a2 *b1*v
25 3x
189 2 21 2 3
+ -----*f(v,v )*f(v,v )*a1*a2 *b1*v + ----*f(v,v )*f(v,v) *a2 *b1*v)/
25 2x x 25 x
3
a1