Nonautonomous Matter-Wave Solitons in a Bose–Einstein Condensate with an External Potential

Abstract

Nonautonomous matter-wave solitons in a Bose–Einstein condensate with an external potential are reported. Via the non-isospectral Ablowitz–Kaup–Newell–Segur system, the Gross–Pitaevskii equation is found to have the double Wronskian solutions. The verification of such solutions is finished through some double Wronskian identities. With the zero-potential Lax pair, the double Wronskian solutions give the nonautonomous N-soliton solutions that contain 2N parameters. For characterizing the asymptotic behavior of the bright two-soliton solutions, the explicit expressions of asymptotic solitons are given. Effects of the linear and harmonic potentials on the bound states between two matter-wave solitons are discussed.