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A new Hamiltonian of α-helical protein molecules is presented according to the mechanism of interaction between their components. We obtain the Raman spectrum of the protein molecules on the basis of the Hamiltonian and quantum transition theory. The coupling intensity between the main chain and side chains of the molecules is obtained by comparing with the laser-Raman spectrum experimentally measured.
We obtain the exact bright and dark solitary wave solutions of the nonlinear Schrodinger equation (NLSE) with the higher-order nonlinearity and the third-order dispersion without any specified conditions, and analyze the features of the solutions. The results show that the higher-order nonlinearity and the third-order dispersion can mutually compensate for a soliton just as the usual self-phase modulation...
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