Non-linear phenomena in nuclei: the antisoliton model for fission

The non-linear solutions of the Modified Korteweg-de Vries (MKdV) equations travel on the nuclear surface of medium-heavy nuclei and generate highly deformed shapes. The cnoidal and soliton solutions provide the existence of rotons as large amplitude collective oscillations. The dynamics is based on the nonlinear equations and Hamiltonian of a realistic liquid drop model (LDM). The antisoliton solutions are obtained through a general formulation of nonrelativistic quantum mechanics in terms of density and current operators. The quantum averaging of the antisoliton pail rotation describes symmetric or asymmetric fission modes. The nuclear asymmetry near the scission point seems to be in qualitative agreement with the general shapes considered in all other phenomenological fission models.