3D skyrmion and knot in two-component Bose–Einstein condensates

•We present 3D Cartesian coordinates analytical result to the coupled nonlinear equation.•These solitonic solutions can form 3D skyrmion and knot in the three-dimensional system.•The solutions can be applied to other physical nonlinear model.

We present exact solutions to the two-component Bose–Einstein condensates by adopting a method of separating the variables, which exhibit nontrivial topology. These solitonic solutions can form 3D skyrmion and knot in the three-dimensional system.