Solution 1 to problem N1t5s10f2


Expressions | Parameters | Inequalities | Relevance | Back to problem N1t5s10f2

Expressions

The solution is given through the following expressions:

q6=0


q5=2*q1


q4=0


q3= - q1


q2=q1


p1= - p2


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:
 q1, 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.
 
{p1,p2,q1}


Relevance for the application:



The equation: 


f = - Df *f*p2 + Df*f *p2
 t      x            x
The symmetry:
                       2
f =Df  *Df*f*q1 + (Df ) *f*q1 - Df *Df*f *q1 + 2*f  *f *f*q1
 s   2x              x            x     x         2x  x
And now in machine readable form:

The system:

df(f(1),t)= - d(1,df(f(1),x))*f(1)*p2 + d(1,f(1))*df(f(1),x)*p2$
The symmetry:
df(f(1),s)=d(1,df(f(1),x,2))*d(1,f(1))*f(1)*q1 + d(1,df(f(1),x))**2*f(1)*q1 - d(
1,df(f(1),x))*d(1,f(1))*df(f(1),x)*q1 + 2*df(f(1),x,2)*df(f(1),x)*f(1)*q1$