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Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

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Abstract

In this paper, we study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. The first-order nonautonomous breather solution of the fourth-order vc-NLS equation is derived. The state transition between nonautonomous breather and nonautonomous multi-peak soliton can be realized when group velocity dispersion (GVD) coefficient is proportional to the fourth-order dispersion (FOD) coefficient. We also display how the higher-order effects influence the nonautonomous multi-peak solitons. Our results show that the velocity and localization of the nonautonomous multi-peak soliton are affected by the FOD coefficient, and the peak number is controlled by the GVD coefficient. Further, we also show the compression effect and motion with variable velocity of nonautonomous multi-peak soliton in two kinds of dispersion management systems. Finally, we reveal the relation between the state transition and the modulation instability (MI) analysis.

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Acknowledgements

We express our sincere thanks to all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant (Nos. 11305060, 11271126, 11705290 and 61505054), by the Fundamental Research Funds of the Central Universities (Project No. 2015ZD16), by China Postdoctoral Science Foundation funded sixtieth batches (No. 2016M602252). Lei Wang put forward the idea of this paper. Lei Wang and Liu-ying Cai contributed all mathematical calculation and physical analysis. Lei Wang and Liu-ying Cai wrote the paper. Xin Wang, Min Li, Yong Liu and Yu-ying Shi polished the language. Liu-ying Cai generated all the figures and was responsible for all simulations.

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Authors and Affiliations

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

    Liu-Ying Cai, Lei Wang, Min Li, Yong Liu & Yu-Ying Shi

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

    Xin Wang

  3. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, 450001, Henan, People’s Republic of China

    Xin Wang

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  1. Liu-Ying Cai
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  2. Xin Wang
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  3. Lei Wang
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  4. Min Li
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Correspondence to Lei Wang.

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Liu-Ying Cai and Lei Wang are co-first authors.

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Cai, LY., Wang, X., Wang, L. et al. Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects. Nonlinear Dyn 90, 2221–2230 (2017). https://doi.org/10.1007/s11071-017-3797-2

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