相干耦合玻色

我们考虑耦合无量纲 Gross-Pitaevskii (GP) 方程，该方程描述了捕获在外部复势中的有效相干耦合玻色-爱因斯坦凝聚态 (BEC)。通过改进的相似变换，得到了可积条件，并将系统简化为一个具有自陡峭和自频移的可积自治三次五次非线性薛定谔（NLS）方程。详细研究了所获得的 NLS 方程的基带调制不稳定性 (MI)。通过耦合 GP 方程的非线性啁啾的精确一阶和二阶异常波解，我们分析研究了基带 MI 存在的参数空间中弱扰动连续波解上异常波的传播动力学。我们的结果表明，人们可以通过控制外部捕获势来操纵物质流氓波的运动。仿真提供了支持证据，表明异常波只能出现在发生基带 MI 的情况下。我们的结果显示了如何通过改变一些解参数（例如振幅参数）来生成多重一阶和二阶恶意波。

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We consider coupled dimensionless Gross-Pitaevskii (GP) equations that describes effective coherently coupled Bose–Einstein condensates (BECs) trapped in external complex potentials. Through a modified similarity transformation, the integrability condition is obtained and the system is reduced to one single integrable autonomous cubic-quintic nonlinear Schrödinger (NLS) equation with self-steepening and self-frequency shift. The baseband modulational instability (MI) for the obtained NLS equation is investigated in details. Through the exact first- and second-order rogue wave solutions with nonlinear chirp of the coupled GP equation, we investigate analytically the propagation dynamics of rogue waves on weakly perturbed continuous wave solutions in the parameter space where the baseband MI exist. Our results show that one can manipulate the motion of matter rogue waves by controlling the external trapping potential. Simulations provide supporting evidence that rogue waves can only emerge in regimes where baseband MI occurs. Our results show how multiplet first- and second-order rogue waves can be generated by varying some solution parameters such as the amplitude parameter.