The Peregrine Soliton (PS) is the most celebrated candidate to rogue waves: extreme oceanic wave events that emerge and vanish without a trace. These monstrous waves are not sailor tales, but a real and frequent threat to the integrity of vessels and other maritime structures, as well as to those onboard.

Fortunately, the mathematical description of deep-water wave phenomena allows us to bring the study of rogue waves to the lab in other fields, such as nonlinear optics or ultracold atoms. In this talk, we will focus on the latter and present the first experimental realization of the PS in a two-component Bose-Einstein condensate.

I will introduce the recent development of a method to calculate the (anti)symmetrized wave functions and energies of the ground and low-lying excited states using the unsupervised machine learning technique. I will also introduce the recent attempts to consider the spin-isospin degrees of freedom and extend them to the Dirac equation.

References:

Tomoya Naito, Hisashi Naito, and Koji Hashimoto. Phys. Rev. Research 5, 033189 (2023)

Chuanxin Wang, Tomoya Naito, Jian Li, and Haozhao Liang. arXiv:2403.16819 [nucl-th]

Chuanxin Wang, Tomoya Naito, Jian Li, and Haozhao Liang. To be submitted