Bright, dark soliton for cubic-quintic nonlinear Schrodinger

[dongsh2]

For a given stationary cubic-quintic nonlinear Schrodinger equation,
EU=-U_XX+G1|U|^2U+G2 |U|^4 U, where X=X(t,x). There are bright and dark solitons. In many references, it is found that there is typo or mistake in dark soliton by substituting their soliton solution to this above eqaution. The bright case is OK, but the dark soliton case is incorrect. Could you please so kind point out where or which reference we can find their correct soliton solutions

Many thanks for your kind help.

 

[DrClaude]

Could you give a reference to a paper where the dark soliton solution is incorrect?