Solution 2 to problem N2f0b1o35w6


Expressions | Parameters | Inequalities | Relevance | Back to problem N2f0b1o35w6

Expressions

The solution is given through the following expressions:

q9=0


q8=0


q7=0


q6=0


    1
q5=---*i*q3
    2


       1
q4= - ---*i*q3
       2


q2=0


q1=0


p3=i*p2


p1=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:
 q11, q10, q3, 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.
 
{q5,

 q3,

 p2,

 2*g0003*q10 + g0007*i*q3 + 2*g0008*q3 + 2*g0010*p2,

 p3,

 2*g0011*q10 + g0015*i*q3 + 2*g0016*q3 + 2*g0018*p2,

 2*g0029*q11 + 2*g0030*q10 + g0035*i*q3 - g0036*i*q3 + 2*g0037*q3}


Relevance for the application:



The equation: 


b =D D b  *p2 + b  *i*p2
 t  1 2 2x       3x
The symmetry:
    1         2                                               1    2
b =---*(D D b) *i*q3 + D D b*b *q3 + D D b  *q10 + b  *q11 - ---*b  *i*q3
 s  2    1 2            1 2   x       1 2 4x        5x        2   x
And now in machine readable form:

The system:

df(b(1),t)=d(1,d(2,df(b(1),x,2)))*p2 + df(b(1),x,3)*i*p2$
The symmetry:
df(b(1),s)=1/2*d(1,d(2,b(1)))**2*i*q3 + d(1,d(2,b(1)))*df(b(1),x)*q3 + d(1,d(2,
df(b(1),x,4)))*q10 + df(b(1),x,5)*q11 - 1/2*df(b(1),x)**2*i*q3$