Superposition Solitons In Two-component Bose-Einstein Condensates

Single-component Bose-Einstein condensate (BEC) has been studied theoretically andexperimentally. The soliton which is a macroscopic excitation of the condensate attracts manypeople’s interest. With the development of experiment techniques, multi-component BECs whichpossess complicated quantum phases and the physical appearance are becoming a hot topic ofinternational researches. In this paper, we obtain the exact one and two superposition soliton(SPS) solutions for the coupled Gross-Pitaevskii (G-P) equations describing two-componentBose-Einstein condensates by Hirota bilinear method. Moreover, their dynamics properties andthe collision of two SPSs are investigated in detail. The main contests of this paper are asfollows:First of all, we introduce the developing history of BEC and the formation of ideal gasBEC.Furthermore, we introduce the dynamics equation of BEC and provide the soliton theoryincluding bright soliton, dark soliton and vector soliton.At last, the Hirota bilinear method is applied to studying two-component BECs which isdescribed by coupled G-P equations. In the applications, the exact one and two SPSs areobtained analytically. We discuss the dynamics properties of SPSs, which show the bright-bright(BB) solitons can be obtained from these results easily. When we have dark-bright (DB) solitonsin the two-component BECs, we can construct SPSs as the new solutions for the corresponding system. We also calculate the energies of the BB solitons, DB solitons and SPSs. It shows thatthe phase separation can be obtained by increasing energy. A detail analysis for dynamicsbehavior of two SPSs shows the collision is elastic.