Chiral nonlinear Schrödinger equation

A nonlinear evolution equation, iψx + ψxx − iλ(ψ*ψx−ψψ*x)ψ = 0, which we name the chiral nonlinear Schrödinger (CNLS) equation is studied. The CNLS equation has two kinds of progressive wave solutions; bright soliton for λυ<0 and dark solition for λυ<0, where υ is the velocity of the envelop. The bright soliton corresponds to the particle while the dark soliton is interpreted as the hole.