Abstract

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 space-time 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 Schrödinger 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 Schrödinger 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.

Department(s)

Physics

Comments

Missouri University of Science and Technology, Grant PHY-2110030

International Standard Serial Number (ISSN)

2469-9934; 2469-9926

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2026 American Physical Society, All rights reserved.

Publication Date

06 Jan 2026

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Physics Commons

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