https://doi.org/10.1140/epjs/s11734-025-01855-x
Regular Article
Asymmetric modulation instability dynamics and its quantitative control in a nonlocal 
-symmetric nonlinear Schrödinger system
1
School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
2
School of Physics, Xidian University, 710071, Xi’an, China
3
State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Received:
26
February
2025
Accepted:
8
August
2025
Published online:
23
August
2025
We numerically investigate two types of asymmetric modulation instability (MI) dynamics in a nonlocal -symmetric nonlinear Schrödinger system, which is excited by a two-frequency perturbation applied to a plane wave. The first type is Akhmediev breather, including left-skewed, right-skewed, and symmetric breathers; the second type is characterized by endless growth dynamics, manifested by the appearance of numerical singularities. By properly extend the linear stability analysis method, we quantitatively predict the types of MI dynamics and their asymmetry. By adjusting the amplitude and phase differences between these two frequency components, we can achieve precise control over the asymmetry of breathers. We also explaining the reasons for their difference from the results in the standard nonlinear Schrödinger system. Our analysis of the MI symmetry is independent of system integrability. Therefore, it is applicable across various nonlinear systems. Our results also provide a theoretical reference for generating asymmetric MI dynamics in PT-symmetric systems.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
