标题： 通过碰撞非均匀玻色-爱因斯坦凝聚体中的平均化构造调幅波 显示英文标题

标题： Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates

摘要： 我们应用平均化方法来分析非线性薛定谔方程中的时空结构，从而研究散射长度在空间中周期变化并穿过零点的准一维碰撞非均匀玻色-爱因斯坦凝聚体的动力学。 通过调整积分常数 c 在某个开区间上，可以证明存在无限多个（正测度集）调幅波（周期和准周期），它们是不稳定的。 最后，一些数值模拟支持我们的结果。 显示英文摘要

摘要： We apply the averaging method to analyze spatio-temportal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering length varying periodically in spatial and crossing zero. Infinitely many (positive measure set) modulated amplitude waves (periodic and quasi-periodic), which are instable, can be proved to exist by adjusting the intergration constant c on some open interval. Finally, some numerical simulations support our results.