Solution 1 to problem N2f0b1o23w2


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

Expressions

The solution is given through the following expressions:

q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


     1
    ---*p2*q1
     2
q5=-----------
       p4


q4=0


q3=0


q2=0


p6=0


p5=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:
 q1, p2, p4

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.
 
{p2,

 g0061*p4 + g0063*p2,

 g0011*q1 + g0013*p4,

 g0023*q1 + g0025*p4,

 p4,

                                         2
 g0035*p2*q1 + 2*g0039*p4*q1 + 2*g0040*p4  + 2*g0042*p2*p4,

 q1,

 g0054*p2 + 2*g0058*p4}


Relevance for the application:



The equation: 


b = - D b*D b*p4 + b *b*p2
 t     2   1        x
The symmetry:
                          1      2
     - D b*D b*b*p4*q1 + ---*b *b *p2*q1
        2   1             2   x
b =--------------------------------------
 s                   p4
And now in machine readable form:

The system:

df(b(1),t)= - d(2,b(1))*d(1,b(1))*p4 + df(b(1),x)*b(1)*p2$
The symmetry:
df(b(1),s)=( - d(2,b(1))*d(1,b(1))*b(1)*p4*q1 + 1/2*df(b(1),x)*b(1)**2*p2*q1)/p4
$