Solution 9 to problem N1t8s14f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t8s14f1

Expressions

The solution is given through the following expressions:


q55=0


q54=0


q53=0


q52=0


q51=0


q50=0


q49=0


q48=0


q47=0


q46=0


q45=0


q44=0


q43=0


q42=0


q41=0


q40=0


q39=0


q38=0


q37=0


q36=0


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


     2*p4*q14
q13=----------
        p3


       2
     p4 *q14
q12=---------
         2
       p3


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q5=0


q4=0


q3=0


q2=0


q1=0


p13=0


p12=0


p11=0


p10=0


p9=0


p8=0


p7=0


p6=0


p5=0


p2=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:

 q14, p4, p3

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.

 
{p3,

 q14,

 g0135*p4 + g0136*p3,

         2                                   2               2              3
 g0045*p3 *q14 + 2*g0046*p3*p4*q14 + g0047*p4 *q14 + g0067*p3 *p4 + g0068*p3 ,

         2                           2
 g0112*p3  + 2*g0113*p3*p4 + g0114*p4 }

Relevance for the application:

The equation:


        2                2
f =(Df ) *f*p3 + Df *(Df) *f*p4
 t    x            x

The symmetry:

         3        2              2     3                       5     2
    (Df ) *Df*f*p3 *q14 + 2*(Df ) *(Df) *f*p3*p4*q14 + Df *(Df) *f*p4 *q14
       x                       x                         x
f =------------------------------------------------------------------------
 s                                     2
                                     p3

And now in machine readable form:

The system:

df(f(1),t)=d(1,df(f(1),x))**2*f(1)*p3 + d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p4$

The symmetry:

df(f(1),s)=(d(1,df(f(1),x))**3*d(1,f(1))*f(1)*p3**2*q14 + 2*d(1,df(f(1),x))**2*d
(1,f(1))**3*f(1)*p3*p4*q14 + d(1,df(f(1),x))*d(1,f(1))**5*f(1)*p4**2*q14)/p3**2$