Solution 2 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


       2
     p5 *q11
q12=---------
         2
       p2


     2*p5*q11
q10=----------
        p2


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


        2
    2*p5 *q11
q2=-----------
         2
       p2


    2*p5*q11
q1=----------
       p2


p6=0


p4=0


p3=p5


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:

 q11, p5, p2

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.

 
{q11,

 p5,

 p2,

 g0028*p5 + g0030*p5 + g0031*p2,

 p3,

                                           2
 2*g0008*p5*q11 + 2*g0009*p2*q11 + g0010*p2 ,

         2           2                             2
 g0015*p5  + g0016*p2  + 2*g0017*p2*p5 + 2*g0025*p5  + 2*g0026*p2*p5}

Relevance for the application:

The equation:


                 2          2
b =Db *Db*p5 + b  *p5 + b *b *p2
 t   x          x        x

The symmetry:

              2                           2         3   2
b =(2*Db *Db*b *p2*p5*q11 + 2*Db *Db*b *p5 *q11 + b  *p5 *q11
 s      x                       x     x            x

           2  2                 4   2        2
     + 2*b  *b *p2*p5*q11 + b *b *p2 *q11)/p2
          x                  x

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*p5 + df(b(1),x)*b(1)**2*
p2$

The symmetry:

df(b(1),s)=(2*d(1,df(b(1),x))*d(1,b(1))*b(1)**2*p2*p5*q11 + 2*d(1,df(b(1),x))*d(
1,b(1))*df(b(1),x)*p5**2*q11 + df(b(1),x)**3*p5**2*q11 + 2*df(b(1),x)**2*b(1)**2
*p2*p5*q11 + df(b(1),x)*b(1)**4*p2**2*q11)/p2**2$