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Dynamics of superregular breathers in the quintic nonlinear Schrödinger equation

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Abstract

In this paper, we consider an extended nonlinear Schrödinger equation that includes fifth-order dispersion with matching higher-order nonlinear terms. Via the modified Darboux transformation and Joukowsky transform, we present the superregular breather (SRB), multipeak soliton and hybrid solutions. The latter two modes appear as a result of the higher-order effects and are converted from a SRB one, which cannot exist for the standard NLS equation. These solutions reduce to a small localized perturbation of the background at time zero, which is different from the previous analytical solutions. The corresponding state transition conditions are given analytically. The relationship between modulation instability and state transition is unveiled. Our results will enrich the dynamics of nonlinear waves in a higher-order wave system.

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Acknowledgements

This work has been supported by the National Major Science and Technology Program for Water Pollution Control and Treatment (No. 2017ZX07101-002), by the National Natural Science Foundation of China under Grant Nos. 11305060, 11705145, 11705290 and 61705006 and by the Fundamental Research Funds of the Central Universities (No. 2018MS048) and by China Postdoctoral Science Foundation funded sixtieth batches (No. 2016M602252).

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  1. Lei Wang and Chong Liu are co-first authors.

Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Bei**g, 102206, People’s Republic of China

    Lei Wang & Xuan Wu

  2. School of Physics, Northwest University, **’an, 710069, People’s Republic of China

    Chong Liu

  3. Shaanxi Key Laboratory for Theoretical Physics Frontiers, **’an, 710069, People’s Republic of China

    Chong Liu

  4. College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, People’s Republic of China

    **n Wang

  5. School of Mathematics and Physics, and Bei**g Key Laboratory for Magneto-Photoelectrical, Composite and Interface Science, University of Science and Technology Bei**g, Bei**g, 100083, People’s Republic of China

    Wen-Rong Sun

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Wang, L., Liu, C., Wu, X. et al. Dynamics of superregular breathers in the quintic nonlinear Schrödinger equation. Nonlinear Dyn 94, 977–989 (2018). https://doi.org/10.1007/s11071-018-4404-x

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