Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensat...Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.展开更多
The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstl...The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.展开更多
基金supported by NSFC under Grant No.12272403Beijing Training Program of Innovation under Grant No.S202410019024。
文摘Introducing PT-symmetric generalized Scarf-Ⅱpotentials into the three-coupled nonlinear Gross-Pitaevskii equations offers a new way to seek stable soliton states in quasi-onedimensional spin-1 Bose-Einstein condensates.In scenarios where the spin-independent parameter c_(0)and the spin-dependent parameter c_(2)vary,we use both analytical and numerical methods to investigate the three-coupled nonlinear Gross-Pitaevskii equations with PT-symmetric generalized Scarf-Ⅱpotentials.We obtain analytical soliton states and find that simply modulating c_(2)may change the analytical soliton states from unstable to stable.Additionally,we obtain numerically stable double-hump soliton states propagating in the form of periodic oscillations,exhibiting distinct behavior in energy exchange.For further investigation,we discuss the interaction of numerical double-hump solitons with Gaussian solitons and observe the transfer of energy among the three components.These findings may contribute to a deeper understanding of solitons in Bose-Einstein condensates with PT-symmetric potentials and may hold significance for both theoretical understanding and experimental design in related physics experiments.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11874324 and 11705164)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LY17A040011,LY17F050011,and LR20A050001)+1 种基金the Foundation of “New Century 151 Talent Engineering” of Zhejiang Province of Chinathe Youth Talent Program of Zhejiang A&F University
文摘The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.
