Vibrational spectra Hamiltonian equation

Aside from solitons, there is a continuous spectrum of torsional modes, or rotons. These excitations are the eigenstates of the linearized Hamiltonian. To obtain their spectrum, one replaces the last term in (7.68) with a harmonic potential. This approximation implies that the vibrational amplitude of a rotor must be small enough compared with the large amplitude motion of a rotor participating in a soliton. The frequencies of rotons obey the dispersion equation ... 

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