Spatial Soliton In The Nonlocal Media With Competing Nonlinearities

During the recent years,the propagation of spatial solitons has drawn considerable attention.However,most previous research of solitons was studied in local nonlinear media which is an ideal research model.In fact,lots of realistic media has a nonlocal nonlinear response,such as plasma,atomic vapors,Bose-Einstein condensates,nematic liquid crystals and so on.Nonlocality has been shown to have a stabilizing effect on nonlinear structure.It also affects the interaction between solitons.Recently,the studies of spatial solitons have been extended to nonlocal media with competing nonlinearities.The competing nonlinearities are induced by different physical processes and contribute to the overall nonlinear response of the medium.Typical examples include simultaneous local and long range interaction in Bose-Einstein condensation,and thermal and orientational nonlinearities in nematic liquid crystal.The competing nonlocal nonlinearities have significant effect on propagation and properties of solitons.The competing nonlinearities can stabilize many complex soliton structures,including vortex solitons with high topological charge as well as one-dimensional multi-hump solitons,which are otherwise unstable in a medium with one type of nonlocal nonlinearity.Competing nonlinearities can also support the fundamental bright and dark solitons.In Chapter 1,we illustrated the historical background of the soliton.The concept and the importance of the solitons,nonlocal medium and competing nonlinearity were also introduced.We derived the theoretical model of solitons in detail.The Lagrangian variational approach and split step fast Fourier transform method are used to investigate the soliton properties.We also introduced the research status of the subject briefly.In Chapter 2,we focused on the interaction of dark solitons under competing cubic nonlinearities with an arbitrary degree of nonlocality.It is shown that the competing self-focusing nonlinearity enhances the repulsive force of the interaction,whereas the competing self-defocusing nonlinearity strengthens the attractive force of the interaction.Besides,the competing second self-defocusing nonlinearity can suppress the strong dispersive waves of the interaction.In Chapter 3,we investigated analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities.It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons,whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton relative distance.In Chapter 4,we investigated systematically the stability of two dimensional vortex solitons in nonlinear media under competing local and nonlocal cubic nonlinearities.When the local cubic nonlinearity is self-focusing,the formation power of the vortex solitons will approach a constant in the limit of strong nonlocality.The long-lived stable vortex solitons can be obtained with moderate degree of nonlocality when the nonlocal cubic nonlinearity is self-focusing.Otherwise,the vortex solitons will suffer from the unstable dynamics,such as splitting,diffraction enhancement,and catastrophic collapse.In the limit of strong degree of nonlocality,the vortex solitons are always unstable.Finally,in Chapter 5 we summarized the main results obtained in this thesis.