Solution 2 to problem N2f1b0o35w7

Expressions | Parameters | Inequalities | Relevance | Back to problem N2f1b0o35w7

Expressions

The solution is given through the following expressions:


q6= - i*q4


q5=q4


q3=i*q4


q2=0


q1=0


p2=i*p1

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:

 q8, q7, q4, 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.

 
{q3,

 q4,

 p1,

 g0011*q7 - g0012*i*q4 + g0013*q4 + g0014*i*q4 + g0016*p1,

 p2,

 g0005*q7 + g0006*q4 + g0007*q4 + g0008*i*q4 + g0010*p1}

Relevance for the application:

The equation:


f =D D f  *p1 + f  *i*p1
 t  1 2 2x       3x

The symmetry:

f =D f*D D f*i*q4 + D f*f *q4 + D D f  *q7 + D D f*D f*q4 - D f*f *i*q4 + f  *q8
 s  2   1 2          2   x       1 2 4x       1 2   1        1   x         5x

And now in machine readable form:

The system:

df(f(1),t)=d(1,d(2,df(f(1),x,2)))*p1 + df(f(1),x,3)*i*p1$

The symmetry:

df(f(1),s)=d(2,f(1))*d(1,d(2,f(1)))*i*q4 + d(2,f(1))*df(f(1),x)*q4 + d(1,d(2,df(
f(1),x,4)))*q7 + d(1,d(2,f(1)))*d(1,f(1))*q4 - d(1,f(1))*df(f(1),x)*i*q4 + df(f(
1),x,5)*q8$