Soliton states of Maxwell’s equations and nonlinear Schrödinger equation

Similarities and fundamental differences between Maxwell’s equations and nonlinear Schrödinger equation in predicting a soliton evolution in a uniform nonlinear anisotropic medium are analyzed. It is found that in some cases, the soliton solutions to the nonlinear Schrödinger equation cannot be recovered from Maxwell’s equations while in others the soliton solutions to Maxwell’s equations are lost from the nonlinear Schrödinger equation through approximation, although there are cases where the soliton solutions to the two sets of the equations demonstrate only quantitative difference. The origin of the differences is also discussed.