The Painlevé Test And Solutions Of The Coupling NLS System For Twin-core Optical Fibers

In this thesis,we consider the following linear coupling nonlinear Schrodinger system with variable coefficients This model arises from the theory of nonlinear optics,which describes the dynam-ics of wave propagation in twin-core optical fibers,under the assumption that the phase velocity difference between the two cores is zero,where for the j-th(j=1,2)core,?j1 denotes the group velocity parameter,?j2 the dispersion parameter,?j the nonlinearity parameter,and c(t)is the linear coupling parameter between the two cores.These parameters can be tuned in the experiments.We prove that when the parameters satisfy the conditions ?11(t)=?21(t),?12(t)=?22(t),?1(t)=?2(t),c(t)=C1(?2(t))2/?22(t),?2(t)=?22(t)/C2??22(t)dt-C3,the system can pass the Painleve test.Under the above condition,we obtain some exact solutions of the system via a transformation and sine-cosine method.Our results are helpful for the understanding the relations among the parameters and the stable transmission of the optical wave.