标题： 扩展的 Gross-Pitaevskii 模型中的畸形波与 Lee-Huang-Yang 修正 显示英文标题

标题： Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction

摘要： 我们探索了一维量子液滴环境中的孤波（RWs）的存在性和动力学生成。通过将时空固定点方案应用于相关的扩展Gross-Pitaevskii方程（eGPE），计算出RWs。确定了随后的RWs与非线性薛定谔方程中的对应物不同的参数区域。为了验证这些孤波图案的可控生成，与超冷原子实验相关，我们采用了两种不同的协议。第一种基于从Riemann初始条件发出的溃坝流的干涉，第二种涉及空间局域波形的梯度灾难。在这个系统中发现了多种可能的RWs，包括类似于Peregrine孤子的波形、其空间周期性变体，即Akhmediev呼吸子，以及其他高阶非线性薛定谔方程的RW解。讨论了对应eGPE RWs形状的关键要素，这些要素可追溯到非可积性和竞争相互作用的存在。我们的结果为在具有竞争相互作用的混合物中探测大量未被探索的类似孤波波形奠定了基础，并且应可被当前的超冷原子实验所实现。 显示英文摘要

摘要： We explore the existence and dynamical generation of rogue waves (RWs) within a one dimensional quantum droplet bearing environment. RWs are computed by deploying a spacetime fixed point scheme to the relevant extended Gross Pitaevskii equation (eGPE). Parametric regions where the ensuing RWs are different from their counterparts in the nonlinear Schroedinger equation are identified. To corroborate the controllable generation, relevant to ultracold atom experiments, of these rogue patterns we exploit two different protocols. The first is based on interfering dam break flows emanating from Riemann initial conditions and the second refers to the gradient catastrophe of a spatially localized waveform. A multitude of possible RWs are found in this system, spanning waveforms reminiscent of the Peregrine soliton, its spatially periodic variants, namely, the Akhmediev breathers, and other higher order RW solutions of the nonlinear Schroedinger equation. Key elements of the shape of the corresponding eGPE RWs traced back to nonintegrability and the presence of competing interactions are discussed. Our results set the stage for probing a multitude of unexplored rogue like waveforms in such mixtures with competing interactions and should be accessible to current ultracold atom experiments.