Solution 1 to problem N1t11s14f2


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t11s14f2

Expressions

The solution is given through the following expressions:

q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q6=0


q4=0


q3=0


q2=0


p7=0


p6=0


p5=0


p4=0


p1=0


    4*p2*q5
q1=---------
     3*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:
 q5, p3, p2

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.
 
{3*g0014*p3 + 4*g0018*p2,g0023*p3 + g0024*p2,p3}


Relevance for the application:



The equation: 


           2            3
f =Df *(Df) *f*p2 + (Df) *f *p3
 t   x                     x
The symmetry:
     4          3               4
    ---*Df *(Df) *f*p2*q5 + (Df) *f *p3*q5
     3    x                        x
f =----------------------------------------
 s                    p3
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)*p2 + d(1,f(1))**3*df(f(1),x)*p3$
The symmetry:
df(f(1),s)=(4/3*d(1,df(f(1),x))*d(1,f(1))**3*f(1)*p2*q5 + d(1,f(1))**4*df(f(1),x
)*p3*q5)/p3$