title: Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity.
abstract: The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning.
authors.affiliation: Department of Applied Mathematics, China Agricultural University, Beijing 100083, People's Republic of China.
authors.forename: Yu-Qin
authors.initials: YQ
authors.lastname: Yao
authors.affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
authors.forename: Ji
authors.initials: J
authors.lastname: Li
authors.affiliation: Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, Chinese Academy of Sciences, Xian 710600, People's Republic of China.
authors.forename: Wei
authors.initials: W
authors.lastname: Han
authors.affiliation: School of Science, Beijing Information Science and Technology University, Beijing 100192, People's Republic of China.
authors.forename: Deng-Shan
authors.initials: DS
authors.lastname: Wang
authors.affiliation: Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
authors.forename: Wu-Ming
authors.initials: WM
authors.lastname: Liu