Solution 1 to problem N1t4s14f1

Expressions | Parameters | Inequalities | Relevance | Back to problem N1t4s14f1

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= - q5


q39=0


        20
q38= - ----*q5
        3


q37=0


q36=0


q35=0


q34= - q5


q33=0


q32=0


q31=0


q30=0


q29=0


        50
q28= - ----*q5
        9


q27=0


q26=0


q25=0


q24=0


q23=0


q22=0


     5
q21=---*q5
     3


q20=0


q19=0


q18=0


        2
q17= - ---*q5
        9


        2
q16= - ---*q12
        9


q15=0


     2
q14=---*q5
     9


q13=0


q11=0


        2
q10= - ---*q5
        3


q9=0


q8=0


q7=0


q6=0


q4=0


q3=0


q2=0


q1=0


p4=0


       4
p3= - ---*p1
       3


p2=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: 
 q12, q5, 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. 
 
{q5,

 p1,

 9*g0019*q5 + 60*g0021*q5 + 9*g0025*q5 + 50*g0031*q5 - 15*g0038*q5 + 2*g0042*q5

  + 2*g0043*q12 - 2*g0045*q5 - 9*g0047*q12 + 6*g0049*q5 - 9*g0054*q5

  + 12*g0059*p1 - 9*g0061*p1,

 p3,

 9*g0077*q5 + 60*g0079*q5 + 9*g0083*q5 + 50*g0089*q5 - 15*g0096*q5 + 2*g0100*q5

  + 2*g0101*q12 - 2*g0103*q5 - 9*g0105*q12 + 6*g0107*q5 - 9*g0112*q5}

Relevance for the application:



The equation: 



               4
f =Df *f*p1 - ---*Df*f *p1
 t   x         3      x


The symmetry: 

            3         2               2         5           3
f =Df  *(Df) *f*q5 - ---*Df  *Df *(Df) *f*q5 + ---*Df  *(Df) *f *q5
 s   3x               3    2x   x               3    2x        x

    2       3            2       2     2                 5
 + ---*(Df ) *Df*f*q5 - ---*(Df ) *(Df) *f *q5 + Df *(Df) *f*q12
    9     x              9     x          x        x

           3           50                        2      6              4
 - Df *(Df) *f  *q5 - ----*Df *Df*f  *f *f*q5 - ---*(Df) *f *q12 - (Df) *f  *q5
     x        2x       9     x     2x  x         9         x              3x

    20      2
 - ----*(Df) *f  *f *f*q5
    3          3x  x


And now in machine readable form: 

The system: 

df(f(1),t)=d(1,df(f(1),x))*f(1)*p1 - 4/3*d(1,f(1))*df(f(1),x)*p1$


The symmetry: 

df(f(1),s)=d(1,df(f(1),x,3))*d(1,f(1))**3*f(1)*q5 - 2/3*d(1,df(f(1),x,2))*d(1,df
(f(1),x))*d(1,f(1))**2*f(1)*q5 + 5/3*d(1,df(f(1),x,2))*d(1,f(1))**3*df(f(1),x)*
q5 + 2/9*d(1,df(f(1),x))**3*d(1,f(1))*f(1)*q5 - 2/9*d(1,df(f(1),x))**2*d(1,f(1))
**2*df(f(1),x)*q5 + d(1,df(f(1),x))*d(1,f(1))**5*f(1)*q12 - d(1,df(f(1),x))*d(1,
f(1))**3*df(f(1),x,2)*q5 - 50/9*d(1,df(f(1),x))*d(1,f(1))*df(f(1),x,2)*df(f(1),x
)*f(1)*q5 - 2/9*d(1,f(1))**6*df(f(1),x)*q12 - d(1,f(1))**4*df(f(1),x,3)*q5 - 20/
3*d(1,f(1))**2*df(f(1),x,3)*df(f(1),x)*f(1)*q5$