Solution 1 to problem N1t4s12f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s12f1

Expressions

The solution is given through the following expressions:


q35=0


q34=0


q33=0


q32=0


q31=0


q30=0


q29=0


q28=0


q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


q18=0


q17=0


q16=0


q15=0


q14=0


q13=0


q11=0


q10=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p4=0


p2=0


    5*p1*q12
q9=----------
       p3

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:

 q12, p3, p1

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.

 
{g0065*p3 + 5*g0068*p1,p1 + p3,g0078*p3 + g0080*p1,p3}

Relevance for the application:

The equation:


f =Df *f*p1 + Df*f *p3
 t   x            x

The symmetry:

              4                5
    5*Df *(Df) *f*p1*q12 + (Df) *f *p3*q12
        x                         x
f =----------------------------------------
 s                    p3

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 + d(1,f(1))*df(f(1),x)*p3$

The symmetry:

df(f(1),s)=(5*d(1,df(f(1),x))*d(1,f(1))**4*f(1)*p1*q12 + d(1,f(1))**5*df(f(1),x)
*p3*q12)/p3$