A Vector Theory on Spatial Solitons in Kerr Media

A new vector theory which concerns the necessary and sufficient conditions of the self-trapping of a linearly polarized light beam in Kerr media is presented after a generalization of Fermat's principle. It is rigidly proven under these conditions that 1+1-dimensional spatial solitons can exist in Kerr media but 2+1-dimensional solitons cannot. A new form of the general equation for 1+1-dimensional solitons in Kerr media is put forward and some of its solutions have been obtained.