Solution 23 to problem e3null

Expressions | Parameters | Relevance | Back to problem e3null

Expressions

The solution is given through the following expressions:


b22=0


b31=0


b32=0


b33=0


c12=0


c13=0


c22=0


c23=0


c33=0


n1=0


n2=0


m1=0


m2=0


m3=0


r6=0


r5=0


r4=0


r2=0


r1=0


q19=0


q18=0


q16=0


q15=0


q14=0


q13=0


q12=0


q11=0


q10=0


q9=0


q8=0


q7=0


q5=0


q4=0


q3=q1


q2=0


p50=0


p49=0


p48=0


p47=p15


p46=0


p45=0


p44=0


p43=0


p42=0


p41=0


p40=0


p39=0


p38=0


p37=0


p36=0


p35=0


p34=0


p33=0


p32=0


p31=0


p30=0


p29=0


p28=p15


p27=0


p26=0


p25=0


p24=0


p23=0


p22=0


p21=0


p20=0


p19=0


p18=0


p17=0


p16=0


p14=0


p13=0


p12=0


p11=0


p9=0


p8=0


p7=p5


p6=0


p4=0


p3=0


p2=0


p1=0


k104=0


k103=0


k101=0


k100=0


k99=0


k98=0


k97=0


k96=0


k95=0


k94=0


k93=0


k92=0


k90=0


k89=0


k88=0


k87=0


k86=0


k85=0


k84=0


k83=0


k82=0


k81=0


k80=0


k79=0


k78=0


k77=0


k76=0


k75=0


k74=0


k73=0


k72=0


k71=0


k70=0


k69=0


k68=0


k67=0


k66=0


k65=0


k64=0


k63=0


k62=0


k61=0


k60=0


k59=0


k58=0


k57=0


k56=0


k55=0


k54=0


k53=0


k52=0


k51=0


k50=0


k49=0


k48=0


k47=0


k46=0


k45=0


k44=0


k43=0


k42=0


k41=0


k40=0


k39=0


k38=0


k37=0


k36=0


k35=0


k34=0


k33=0


k32=0


k31=0


k30=0


k28=0


k27=0


k26=0


k25=0


k24=0


k23=0


k21=0


k20=0


k19=0


k18=0


k17=0


k16=0


k14=0


k13=0


k12=k10


k11=0


k9=0


k8=0


k7=0


k6=0


k5=k1


k4=0


k3=2*k1


k2=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:

 r3,q1,p15,p10,k10,k1,n3,p5,a33,a22

Relevance for the application:

The following expression INT is a first

integral for the Hamiltonian HAM:

          2         2         2
HAM=a22*u1  + a22*u2  + a33*u3  + n3*u3

         4          2   2        4         2   2         2   2         3
INT=k1*u1  + 2*k1*u1 *u2  + k1*u2  + k10*u1 *u3  + k10*u2 *u3  + p10*u3

                2            2            2        2           2           2
     + p15*u3*v1  + p15*u3*v2  + p15*u3*v3  + p5*u1 *u3 + p5*u2 *u3 + q1*u1

            2
     + q1*u2  + r3*u3



And again in machine readable form:



HAM=a22*u1**2 + a22*u2**2 + a33*u3**2 + n3*u3$

INT=k1*u1**4 + 2*k1*u1**2*u2**2 + k1*u2**4 + k10*u1**2*u3**2 + k10*u2**2*u3**2 +
 p10*u3**3 + p15*u3*v1**2 + p15*u3*v2**2 + p15*u3*v3**2 + p5*u1**2*u3 + p5*u2**2
*u3 + q1*u1**2 + q1*u2**2 + r3*u3$