Solitons in the Calogero-Sutherland collective-field model

In the Bogomolʹnyi limit of the Calogero-Sutherland collective-field model we find static-soliton solutions. The solutions of the equations of motion are moving solitons, having no static limit for λ > 1. They behave like holes and lumps, depending on the value of the statistical parameter λ. We interpret these soliton solutions as effectively made of one quasi-particle and one quasi-hole excitation.