Solution 1 to problem N1t7s10b4+5

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t7s10b4+5

Expressions

The solution is given through the following expressions:


q21=0


q20=0


q19=0


q18=0


        1
q17= - ---*q1
        2


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


       1
q6= - ---*q1
       2


q5=0


q4=0


q3=0


q2=0


p10=0


p8=p9


p7=0


p6=0


p5=0


p3=0


p2=p9


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, p4, p9

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.

 
{p4,p9,g0008*q1 + g0009*p9,q1,p8}

Relevance for the application:

The system:


b(1) =Db(2)*Db(1)*p9 + b(1) *b(2)*p9
    t                      x

          3
b(2) =b(1) *p4 + b(2) *b(2)*p9
    t                x

The symmetry:

          1            2
b(1) = - ---*b(1) *b(1) *q1
    s     2      x

                             1            2
b(2) =Db(2)*Db(1)*b(1)*q1 - ---*b(2) *b(1) *q1
    s                        2      x

And now in machine readable form:

The system:

df(b(1),t)=d(1,b(2))*d(1,b(1))*p9 + df(b(1),x)*b(2)*p9$

df(b(2),t)=b(1)**3*p4 + df(b(2),x)*b(2)*p9$

The symmetry:

df(b(1),s)= - 1/2*df(b(1),x)*b(1)**2*q1$

df(b(2),s)=d(1,b(2))*d(1,b(1))*b(1)*q1 - 1/2*df(b(2),x)*b(1)**2*q1$