In[]:=
ClearAll[A1,A2,B1,B2,n,Jx,Jz,k1,k2,wc,wa,λ]​​​​vars={A1,A2,B1,B2,n,Jx,Jz};​​​​assumptions=k1>0&&k2>0&&wc>0&&wa>0&&λ>0;​​​​eq1=-(k1/2)*A1+wc*A2-2λJxA2-k2*(2nA1+B1+B2A2-2A1^3-2A1A2^2)==0;​​​​eq2=wc*A1+(k1/2)*A2+2λJxA1+k2*(2nA2+B2A1-B1A2-2A1^2A2-2A2^3)==0;​​​​eq3=-k1*B1+2wc*B2-2k2*(3nB1-2A1^4+2A2^4)==0;​​​​eq4=-k1*B2+2wc*B1-4λJxn-2k2*(3nB2-4A1^3A2-4A1A2^3)==0;​​​​eq5=4λJxB2+k1n+k2*(4n^2-4A1^4-4A2^4-8A1^2A2^2+2B1^2+2B2^2)==0;​​​​eq6=wa*Jx-2λJzB1==0;​​​​eq7=Jx^2+Jz^2==1;​​​​eqs={eq1,eq2,eq3,eq4,eq5,eq6,eq7};​​
sol=Solve[eqs,vars](*?Iabortedcomputation!!!*)​​
Out[]=
$Aborted
(*-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------*)
In[]:=
params={k1->1,k2->1,wc->1,wa->1,λ->1};​​​​S=NSolve[(eqs/.params),vars,Reals]​​
Out[]=
{{A13.86977,A2-1.20862,B110.4301,B2-7.75635,n13.7828,Jx0.998853,Jz0.0478831},{A12.2735,A2-1.59675,B12.64163,B2-10.1838,n3.65016,Jx0.982554,Jz0.185975},{A1-2.31418,A21.3399,B12.39443,B2-5.15067,n6.20428,Jx0.978886,Jz0.204409},{A12.59864,A20.0187934,B15.46652,B21.04633,n5.45851,Jx-0.995843,Jz-0.0910857},{A1-1.54357,A21.18969,B10.36289,B2-5.34391,n1.67349,Jx0.587381,Jz0.809311},{A11.72298,A2-0.476663,B13.67226,B2-0.922674,n1.34013,Jx-0.990858,Jz-0.134911},{A11.01764,A2-1.13722,B1-1.20876,B2-3.57378,n1.14981,Jx0.924065,Jz-0.382236},{A11.04528,A20.779695,B11.29043,B22.60207,n0.931302,Jx-0.932451,Jz-0.361296},{A1-0.654964,A2-1.12535,B1-0.151049,B22.53285,n0.510091,Jx-0.289189,Jz0.957272},{A1-0.456317,A2-1.13213,B1-1.96603,B22.19896,n0.00287583,Jx-0.96915,Jz0.246473},{A1-0.365948,A2-0.886509,B1-0.0545606,B21.14681,n0.154659,Jx0.108477,Jz-0.994099},{A10.500915,A2-0.766472,B1-0.601215,B2-1.10168,n0.757035,Jx0.768858,Jz-0.63942},{A1-0.891079,A20.405017,B10.108719,B2-1.08821,n0.197919,Jx-0.212474,Jz-0.977167},{A10.0221547,A20.398573,B10.676028,B20.875108,n0.239941,Jx-0.80399,Jz-0.594643},{A10.0221547,A20.398573,B10.676028,B20.875108,n0.239941,Jx-0.80399,Jz-0.594643},{A1-0.853423,A20.147239,B10.614827,B20.509088,n0.684022,Jx-0.775834,Jz-0.630937},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz-1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz-1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz-1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz-1.},{A10,A20,B10,B20,n0,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz-1.},{A10,A20,B10,B20,n0,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n0,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz-1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz-1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz1.},{A10,A20,B10,B20,n-0.25,Jx0,Jz-1.},{A10.00183666,A20.0424192,B10.0515672,B2-0.011242,n-0.239377,Jx-0.10259,Jz-0.994724},{A10.00183666,A20.0424192,B10.0515672,B2-0.011242,n-0.239377,Jx-0.10259,Jz-0.994724},{A10.00183666,A20.0424192,B10.0515672,B2-0.011242,n-0.239377,Jx-0.10259,Jz-0.994724},{A10.00348501,A2-0.066005,B1-0.0517193,B20.0113169,n-0.23936,Jx0.10289,Jz-0.994693},{A1-0.0399246,A2-0.431528,B1-0.152451,B20.0918684,n-0.215907,Jx0.291647,Jz-0.956526}}
Length[S](*therearenoanalyticalsolutionstothe41stdegreeequation!!!Wedon'thavesuchmathematicaltools.Onlynumericallyyoucansolve.*)
Out[]=
41
In[]:=
S//MatrixForm
Out[]//MatrixForm=
A13.86977
A2-1.20862
B110.4301
B2-7.75635
n13.7828
Jx0.998853
Jz0.0478831
A12.2735
A2-1.59675
B12.64163
B2-10.1838
n3.65016
Jx0.982554
Jz0.185975
A1-2.31418
A21.3399
B12.39443
B2-5.15067
n6.20428
Jx0.978886
Jz0.204409
A12.59864
A20.0187934
B15.46652
B21.04633
n5.45851
Jx-0.995843
Jz-0.0910857
A1-1.54357
A21.18969
B10.36289
B2-5.34391
n1.67349
Jx0.587381
Jz0.809311
A11.72298
A2-0.476663
B13.67226
B2-0.922674
n1.34013
Jx-0.990858
Jz-0.134911
A11.01764
A2-1.13722
B1-1.20876
B2-3.57378
n1.14981
Jx0.924065
Jz-0.382236
A11.04528
A20.779695
B11.29043
B22.60207
n0.931302
Jx-0.932451
Jz-0.361296
A1-0.654964
A2-1.12535
B1-0.151049
B22.53285
n0.510091
Jx-0.289189
Jz0.957272
A1-0.456317
A2-1.13213
B1-1.96603
B22.19896
n0.00287583
Jx-0.96915
Jz0.246473
A1-0.365948
A2-0.886509
B1-0.0545606
B21.14681
n0.154659
Jx0.108477
Jz-0.994099
A10.500915
A2-0.766472
B1-0.601215
B2-1.10168
n0.757035
Jx0.768858
Jz-0.63942
A1-0.891079
A20.405017
B10.108719
B2-1.08821
n0.197919
Jx-0.212474
Jz-0.977167
A10.0221547
A20.398573
B10.676028
B20.875108
n0.239941
Jx-0.80399
Jz-0.594643
A10.0221547
A20.398573
B10.676028
B20.875108
n0.239941
Jx-0.80399
Jz-0.594643
A1-0.853423
A20.147239
B10.614827
B20.509088
n0.684022
Jx-0.775834
Jz-0.630937
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz-1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz-1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz-1.
A10
A20
B10
B20
n-0.25
Jx0
Jz-1.
A10
A20
B10
B20
n0
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz-1.
A10
A20
B10
B20
n0
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n0
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz-1.
A10
A20
B10
B20
n-0.25
Jx0
Jz-1.
A10
A20
B10
B20
n-0.25
Jx0
Jz1.
A10
A20
B10
B20
n-0.25
Jx0
Jz-1.
A10.00183666
A20.0424192
B10.0515672
B2-0.011242
n-0.239377
Jx-0.10259
Jz-0.994724
A10.00183666
A20.0424192
B10.0515672
B2-0.011242
n-0.239377
Jx-0.10259
Jz-0.994724
A10.00183666
A20.0424192
B10.0515672
B2-0.011242
n-0.239377
Jx-0.10259
Jz-0.994724
A10.00348501
A2-0.066005
B1-0.0517193
B20.0113169
n-0.23936
Jx0.10289
Jz-0.994693
A1-0.0399246
A2-0.431528
B1-0.152451
B20.0918684
n-0.215907
Jx0.291647
Jz-0.956526