model. For Laughlin and Halperin states, which can be seen as solitonic wavefunction, we construct the corresponding Hamiltonians in the same manner as CS model. We obtain their bosonic and fermionic representations. The explicit solutions, e.g. excitations and eigenvalues, are exactly solved. The integrability of Laughlin state, is the same as that of CS model, while for Halperin state, the integrability is determined also by the triangularization nature of the Hamiltonian.

There are several problems worthy of exploring in the future. Firstly, though the integrability in this article are inherited from free fermions, it is not clear to the authors that how to construct the integrable hierarchies. In soliton theory, the integrable hierarchy can be determined by the Lax operators. The Lax method is not the expected one for solving the problem since there are in general integration operators (the pseudo-differential operators) additional to usual differential operators. A possible solution may be the inverse scattering method, which will relate the integrable hierarchy to the inverse scattering equation[@das1989integrable]. This hierarchy tells us how integral of motions can be constructed by a recursive relation. A higher level integral of motion determines a refiner excitation structure of the model[@jimbo1983solitons]. Secondly, for FQHEs, people 