Research On Soliton Solutions Of Gross-Pitaevskii Equations

This thesis is mainly concerned with the stationary soliton so-lutionsofthreekindsofGross-Pitaevskiiequations(GPequationsforshort)including the existence, the persistence and the analytical expression of thesolution. The obtained conclusions haven’t been found in the known refer-ences, and so they laid the foundation for the further study on the stabilityof soliton solutions. The main contents are as follows:The first chapter, we briefly introduce the background and purpose ofthis thesis, primary tools and thesis’s main work.The second chapter, we investigate the analytical expression and thepersistence of the stationary soliton solutions of the GP equations with theoptical lattice potential and the self focusing nonlinear term.The third chapter, we investigate the analytical expression and persis-tenceofthestationarysolitonsolutionsoftheGPequationswiththeopticallattice potential and the self de-focusing nonlinear term.The fourth chapter, we rigorously prove the existence of the stationarysoliton solutions of the GP equations with the Gaussian potential and selfde-focusing nonlinear term.