Solution 1 to problem N2f0b1o35w4

Expressions | Parameters | Inequalities | Relevance | Back to problem N2f0b1o35w4

Expressions

The solution is given through the following expressions:


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


     1
    ---*p1*q1
     2
q8=-----------
       p3


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


p5=0


p4=0


p2=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:

 q1, p1, p3

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing.

 
{g0027*q1 + g0029*p3,

 g0013*q1 + g0015*p3,

 p3,

                                         2
 g0037*p1*q1 + 2*g0044*p3*q1 + 2*g0045*p3  + 2*g0047*p1*p3,

 q1,

 g0056*p1 + 2*g0063*p3,

 g0066*p3 + g0068*p1}

Relevance for the application:

The equation:


b = - D b*D b*p3 + b *b*p1
 t     2   1        x

The symmetry:

                          1      2
     - D b*D b*b*p3*q1 + ---*b *b *p1*q1
        2   1             2   x
b =--------------------------------------
 s                   p3

And now in machine readable form:

The system:

df(b(1),t)= - d(2,b(1))*d(1,b(1))*p3 + df(b(1),x)*b(1)*p1$

The symmetry:

df(b(1),s)=( - d(2,b(1))*d(1,b(1))*b(1)*p3*q1 + 1/2*df(b(1),x)*b(1)**2*p1*q1)/p3
$