中文摘要：

研究了（1＋1）维的变系数Gross-Pitaevskii方程,获得了该方程的精确畸形波解.基于该精确畸形波解,深入研究了非自治物质畸形波在随时间指数变化的相互作用下的传播动力学行为,发现非自治畸形波除具有＂来无影、去无踪＂的不可预测特性外,也可实现完全激发、抑制激发以及维持激发等操控.研究表明,畸形波操控的关键是对累积时间的最大值T（max）与峰值位置T0（或TⅠ,TⅡ）值大小关系的调节.当T（max）〉T0（或TⅠ,TⅡ）时畸形波被快速地完全激发,热原子团中的原子增加到凝聚体中.当Tmax〈T0（或TⅠ,TⅡ）时畸形波没有充足的时间来激发而被抑制甚至消失，凝聚体中的原子减少．这些结果在理论和实际应用上具有启迪意义．

英文摘要：

We study a（1＋1）-dimensional variable-coefficient Gross-Pitaevskii equation with parabolic potential.A similarity transformation connecting the variable-coefficient Gross-Pitaevskii equation with the standard nonlinear Schrodinger equation is constructed.According to this transformation and solutions of the standard nonlinear Schrodinger equation,we obtain exact rogue wave solutions of variable-coefficient Gross-Pitaevskii equation with parabolic potential.In this solution,a Galilean transformation is used such that the center of optical pulse is Xc=v（T-T0） while the Galilean transformation was not used in previous analysis.By the Galilean transformation,the parameter T0 is added into the solution.It is found that the parameter T0 is important to control the excitations of rogue waves.Moreover,the parameters α1 and α2 in solution are complex parameters which can modulate the behaviors of rogue waves.If they are restricted to real numbers,we can obtain some well-known rogue wave solutions.If the parameter α2=-1/12,we can have a second-order rogue wave solution.If the parameter α2 is a complex number,the solution can describe rogue wave triplets.Here two kinds of rogue wave triplets,namely,rogue wave triplets Ⅰ and Ⅱ are presented.For rogue wave triplet I,at first,two first-order rogue waves on each side are excited,and then a first-order rogue wave in the middle is excited with the increase of time.On the contrary,for rogue wave triplet Ⅱ,a first-order rogue wave in the middle is initially excited,and then two first-order rogue waves on each side are excited with the increase of time.From these solutions,the controls for the excitations of rogue waves,such as the restraint,maintenance and postponement,are investigated in a system with an exponential-profile interaction.In this system,by modulating the relation between the maximum of accumulated time T（max） and the peak time T0（or TⅠ,TⅡ）,we realize the controls of rogue waves.When T（max） 〉T0（or TⅠ,TⅡ）,rogue wave is excit