Solution 1 to problem N2f0b1o23w1

Expressions | Parameters | Inequalities | Relevance | Back to problem N2f0b1o23w1

Expressions

The solution is given through the following expressions:


q17=0


q16=0


q15=0


q14=0


q13=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


    2*p1*q12
q3=----------
       p3


q2=0


q1=0


p6=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:

 q12, 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.

 
{q3,

 q12,

 2*g0025*q12 + g0030*p3,

 2*g0011*q12 + g0016*p3,

 p1,

 p3,

 g0070*p3 + g0072*p1,

                                         2
 g0034*p3*q12 + 2*g0043*p1*q12 + g0047*p3  + g0049*p1*p3,

 g0055*p3 + 2*g0064*p1}

Relevance for the application:

The equation:


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

The symmetry:

                  3              4
     - 2*D b*D b*b *p1*q12 + b *b *p3*q12
          2   1               x
b =---------------------------------------
 s                   p3

And now in machine readable form:

The system:

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

The symmetry:

df(b(1),s)=( - 2*d(2,b(1))*d(1,b(1))*b(1)**3*p1*q12 + df(b(1),x)*b(1)**4*p3*q12)
/p3$