Fermi Quantum Promotion Derivative For Nonlinear Schr? Dinger Model Integrable

In this thesis , the integrability of generalized multi-component fermi quantum derivative nonlinear Schrodinger (DNLS) model has been studied by using the quantum inverse scattering method (algebraic Bethe Ansatz method). With the help of Lax operator, the monodromy matrix is constructed. And by using the quantum inverse scattering method, it has been shown that the monodromy matrix satisfies the quantum Yang-Baxter equation(QYBE) on both a finite interval and an infinite interval. So the integrability of this model is proved. Through the commutation relations among the elements of monodromy matrix listed by the quantum the Yang-Baxter equation , the eigenvalues and the eigenvectors of the model can also be obtained.The thesis comes in three parts. The first chapter is a brief introduction of the background of the integrable system and the newest developments about the nonlinear Schrodinger (NLS) model and the derivative nonlinear Schrodinger model. In the second chapter, the boson nonlinear Schrodinger model and the integrability of generalized two-component fermi quantum derivative nonlinear Schrodinger model are studied briefly. And in the last chapter the integrability of generalized multi-component fermi quantum derivative nonlinear schrodinger model is studied in detail.