Solution 5 to problem l1o23
Expressions |
Parameters |
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Back to problem l1o23
Expressions
The solution is given through the following expressions:
3 2
---*a4*a8 *b1
4
b21=---------------
3
a6
3
---*a4*a8*b1
2
b20=--------------
2
a6
b19=0
3 3
- ---*a8 *b1
4
b18=---------------
3
a6
3 2
- ---*a8 *b1
2
b17=---------------
2
a6
2
- 3*a8 *b1
b16=-------------
2
a6
- 3*a8*b1
b15=------------
a6
- 3*a8*b1
b14=------------
a6
3
- ---*a8*b1
2
b13=--------------
a6
b12= - 2*b1
b11=0
b10=0
- 3*a4*a8*b1
b9=---------------
2
a6
3
- ---*a4*a8*b1
2
b8=-----------------
2
a6
- 3*a4*b1
b7=------------
a6
- 3*a4*b1
b6=------------
a6
b5=0
2
3*a8 *b1
b4=----------
2
a6
3*a8*b1
b3=---------
a6
3*a8*b1
b2=---------
a6
1
- ---*a4*a8
4
a10=--------------
a6
1 2
---*a8
4
a9=---------
a6
1
a7=---*a8
2
a5=0
a3=0
a2=0
a1=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,a4,a8,a6
Relevance for the application:
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df(u,t)=f(v,v )*a4
x
2 2 3
df(u,s)=(u *a6 *b1 + 3*u *a6*a8*b1*u + 3*u *a6*a8*b1 - ---*u *f(v,v)*a4*a8*b1
3x 2x x 2 x
2 2
+ 3*u *a8 *b1*u - 3*f(v ,v )*a4*a6*b1 - 3*f(v,v )*a4*a6*b1
x x x 2x
2
- 3*f(v,v )*a4*a8*b1*u)/a6
x
df(v,t)=
1 2 1 1 2 2
---*u *a6*a8*v + v *a6 + v *a6*a8*u - ---*f(v,v)*a4*a8*v + ---*a8 *u *v
2 x 2x x 4 4
---------------------------------------------------------------------------
a6
3 2 2 2
df(v,s)=( - ---*u *a6 *a8*b1*v - 3*u *v *a6 *a8*b1 - 3*u *a6*a8 *b1*u*v
2 2x x x x
3 2 3 2 2
- 2*v *a6 *b1 - 3*v *a6 *a8*b1*u - ---*v *a6*a8 *b1*u
3x 2x 2 x
3 3 2
+ ---*f(v,v )*a4*a6*a8*b1*v + ---*f(v,v)*a4*a8 *b1*u*v
2 x 4
3 3 3 3
- ---*a8 *b1*u *v)/a6
4
df(u,t)=f(v,df(v,x))*a4$
df(u,s)=(df(u,x,3)*a6**2*b1 + 3*df(u,x,2)*a6*a8*b1*u + 3*df(u,x)**2*a6*a8*b1 - 3
/2*df(u,x)*f(v,v)*a4*a8*b1 + 3*df(u,x)*a8**2*b1*u**2 - 3*f(df(v,x),df(v,x))*a4*
a6*b1 - 3*f(v,df(v,x,2))*a4*a6*b1 - 3*f(v,df(v,x))*a4*a8*b1*u)/a6**2$
df(v,t)=(1/2*df(u,x)*a6*a8*v + df(v,x,2)*a6**2 + df(v,x)*a6*a8*u - 1/4*f(v,v)*a4
*a8*v + 1/4*a8**2*u**2*v)/a6$
df(v,s)=( - 3/2*df(u,x,2)*a6**2*a8*b1*v - 3*df(u,x)*df(v,x)*a6**2*a8*b1 - 3*df(u
,x)*a6*a8**2*b1*u*v - 2*df(v,x,3)*a6**3*b1 - 3*df(v,x,2)*a6**2*a8*b1*u - 3/2*df(
v,x)*a6*a8**2*b1*u**2 + 3/2*f(v,df(v,x))*a4*a6*a8*b1*v + 3/4*f(v,v)*a4*a8**2*b1*
u*v - 3/4*a8**3*b1*u**3*v)/a6**3$