Solution 3 to problem N2f0b1o23w2


Expressions | Parameters | Inequalities | Relevance | Back to problem N2f0b1o23w2

Expressions

The solution is given through the following expressions:

         4    2
      - ---*p5 *q5
         3
q15=---------------
            2
          p2


q14=0


     p5*q5
q13=-------
      p2


q12=0


q11=0


      - p5*q5
q10=----------
        p2


q9=0


q8=0


q7=0


q6=0


    2*p5*q5
q4=---------
      p2


q3=0


    2*p5*q5
q2=---------
      p2


q1=0


p6=0


p4=0


p3=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:
 q5, 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.
 
{q5,

 p2,

 p5,

 g0016*q5 - g0018*q5 + 2*g0021*q5 + 2*g0022*q5 + g0024*p2,

 g0004*q5 - g0006*q5 + 2*g0009*q5 + 2*g0010*q5 + g0012*p2,

 g0060*p5 + g0063*p2,

 g0027*p5*q5 - g0030*p5*q5 + g0035*p2*q5 + 2*g0036*p5*q5 + 2*g0038*p5*q5

            2
  + g0042*p2 ,

           2                                             2
 4*g0044*p5  - 3*g0046*p2*p5 + 3*g0049*p2*p5 - 3*g0054*p2  - 6*g0055*p2*p5

  - 6*g0057*p2*p5}


Relevance for the application:



The equation: 


b =D D b *p5 + b *b*p2
 t  1 2 x       x
The symmetry:
b =( - D b*D b *p2*p5*q5 - D b *D b*p2*p5*q5 + 2*D D b*b *p2*p5*q5
 s      2   1 x             2 x  1                1 2   x

                              4        2          2   2       2
     + 2*D D b *b*p2*p5*q5 - ---*b  *p5 *q5 + b *b *p2 *q5)/p2
          1 2 x               3   3x           x
And now in machine readable form:

The system:

df(b(1),t)=d(1,d(2,df(b(1),x)))*p5 + df(b(1),x)*b(1)*p2$
The symmetry:
df(b(1),s)=( - d(2,b(1))*d(1,df(b(1),x))*p2*p5*q5 - d(2,df(b(1),x))*d(1,b(1))*p2
*p5*q5 + 2*d(1,d(2,b(1)))*df(b(1),x)*p2*p5*q5 + 2*d(1,d(2,df(b(1),x)))*b(1)*p2*
p5*q5 - 4/3*df(b(1),x,3)*p5**2*q5 + df(b(1),x)*b(1)**2*p2**2*q5)/p2**2$