This is true in general : nonlinear Hartree equations never have an influence on the centre of mass.
2.
The presence of the \ pm sign in the Appleton Hartree equation gives two separate solutions for the refractive index.
3.
In 1929 Taylor returned to the UK and took up a post as Scientific Officer at the Radio Research Station in Slough, Berkshire ( part of the UK Appleton-Hartree Equation.