Solution 7 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


      - p7*q12
q29=-----------
        p4


            2
      - 2*p7 *q12
q28=--------------
           2
         p4


q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


q21=0


q20=0


q19=0


     p7*q12
q18=--------
       p4


q16=0


q15=0


q14=0


     p7*q12
q13=--------
       p4


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= - p7


p11=0


p10=0


p9=0


p8=0


p6=0


p5=0


p3=0


p2=0


p1=0


       2
     p7 *q12
q17=---------
         2
       p4

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, p4, p7

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. 
 
                         2                         2                         2
{g0097*p4*p7 + 2*g0098*p7  - g0108*p4*p7 - g0109*p7  - g0113*p4*p7 - g0114*p4 ,

 g0127*p7 - g0132*p7 - g0135*p4,

 p4}

Relevance for the application:



The equation: 



           2
f =Df *(Df) *f*p4 + Df *Df*f *p7 - f  *f *f*p7
 t   x                x     x       2x  x


The symmetry: 

         2     3                    2     2      2               5     2
f =((Df ) *(Df) *f*p4*p7*q12 + (Df ) *(Df) *f *p7 *q12 + Df *(Df) *f*p4 *q12
 s     x                          x          x             x

               4                                    2
     + Df *(Df) *f *p4*p7*q12 - 2*Df *Df*f  *f *f*p7 *q12
         x        x                 x     2x  x

           3                       2
     - (Df) *f  *f *f*p4*p7*q12)/p4
              2x  x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,df(f(1),x))*d(1,f(1))**2*f(1)*p4 + d(1,df(f(1),x))*d(1,f(1))*df(f
(1),x)*p7 - df(f(1),x,2)*df(f(1),x)*f(1)*p7$


The symmetry: 

df(f(1),s)=(d(1,df(f(1),x))**2*d(1,f(1))**3*f(1)*p4*p7*q12 + d(1,df(f(1),x))**2*
d(1,f(1))**2*df(f(1),x)*p7**2*q12 + d(1,df(f(1),x))*d(1,f(1))**5*f(1)*p4**2*q12 
+ d(1,df(f(1),x))*d(1,f(1))**4*df(f(1),x)*p4*p7*q12 - 2*d(1,df(f(1),x))*d(1,f(1)
)*df(f(1),x,2)*df(f(1),x)*f(1)*p7**2*q12 - d(1,f(1))**3*df(f(1),x,2)*df(f(1),x)*
f(1)*p4*p7*q12)/p4**2$