Solution 9 to problem l1o35
Expressions |
Parameters |
Relevance |
Back to problem l1o35
Expressions
The solution is given through the following expressions:
b74=0
b73=0
b72=0
b71=0
b70=0
b69=0
b68=0
b67=0
b66=0
b65=0
b64=0
b63=0
b62=0
b61=0
b60=0
b59=0
b58=0
a14*a6*b1
b57=-----------
2
a1
b56=0
b55=0
b54=0
b53=0
b52=0
b51=0
b50=0
b49=0
b48=0
b47=0
b46=0
3 2
---*a14 *b1
2
b45=-------------
2
a1
b44=0
b43=0
b42=0
b41=0
b40=0
b39=0
a14*b1
b38=--------
a1
b37=0
b36=0
b35=0
b34=0
b33=0
b32=0
b31=0
b30=0
b29=0
b28=0
b27=0
b26=0
b25=0
b24=0
b23=0
b22=0
b21=0
b20=0
b19=0
b18=0
3*a14*a6*b1
b17=-------------
2
a1
b16=0
b15=0
b14=0
2*a6*b1
b13=---------
a1
2*a6*b1
b12=---------
a1
b11=0
b10=0
b9=0
b8=0
5 2
---*a14 *b1
2
b7=-------------
2
a1
b6=0
b5=0
5
---*a14*b1
2
b4=------------
a1
5*a14*b1
b3=----------
a1
b2=0
a21=0
a20=0
a19=0
a18=0
a17=0
a16=0
a15=0
a13=0
a12=0
a11=0
a10=0
a9=0
a8=0
a7=0
a5=0
a4=0
3
a3=---*a14
2
a2=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,a6,a14,a1
Relevance for the application:
The solution given above tells us that the system {u_s, v_s}
is a higher order symmetry for the lower order system {u_t,v_t}
where u=u(t,x) is a scalar function, v=v(t,x) is a vector
function of arbitrary dimension and f(..,..) is the scalar
product between two such vectors:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2
u =u *a1 + ---*u *a14 + f(v ,v )*a6
t 3x 2 x x x
v =u *v *a14
t x x
2 5 2 5 3 2
u =(u *a1 *b1 + 5*u *u *a14*a1*b1 + ---*u *a14*a1*b1 + ---*u *a14 *b1
s 5x 3x x 2 2x 2 x
+ 3*u *f(v ,v )*a14*a6*b1 + 2*f(v ,v )*a1*a6*b1 + 2*f(v ,v )*a1*a6*b1)/
x x x 2x 2x x 3x
2
a1
3 2 2
u *v *a14*a1*b1 + ---*u *v *a14 *b1 + v *f(v ,v )*a14*a6*b1
3x x 2 x x x x x
v =---------------------------------------------------------------
s 2
a1