Solution 3 to problem N1f0b1o35w2

Expressions | Parameters | Inequalities | Relevance | Back to problem N1f0b1o35w2

Expressions

The solution is given through the following expressions:


q16=0


q15=0


q14=0


q13=0


      1           1
     ---*p3*q2 + ---*p5*q2
      3           6
q12=-----------------------
              p5


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q1=0


p6=0


p4=0


p2=0


p1=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:

 q2, p5, 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.

 
{2*g0015*p3 + g0015*p5 + 6*g0025*p5,q2,g0028*p5 + g0030*p3,g0008*q2 + g0010*p5,

 p5}

Relevance for the application:

The equation:


                 2
b =Db *Db*p5 + b  *p3
 t   x          x

The symmetry:

                       1    3          1    3
    Db *Db*b *p5*q2 + ---*b  *p3*q2 + ---*b  *p5*q2
      x     x          3   x           6   x
b =-------------------------------------------------
 s                        p5

And now in machine readable form:

The system:

df(b(1),t)=d(1,df(b(1),x))*d(1,b(1))*p5 + df(b(1),x)**2*p3$

The symmetry:

df(b(1),s)=(d(1,df(b(1),x))*d(1,b(1))*df(b(1),x)*p5*q2 + 1/3*df(b(1),x)**3*p3*q2
 + 1/6*df(b(1),x)**3*p5*q2)/p5$