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Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity

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Abstract

In this work, we consider a nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity, which works as a model for the propagation of ultrashort pulse in optical fiber and also corresponds to one-dimensional anisotropic Heisenberg ferromagnetic spin chain. Introducing a Galilean transformation, we transform the model into a fifth-order complex modified KdV equation, the integrability of which has been considered in the AKNS technique framework. The N-fold Darboux transformation for the model is derived in terms of the gauge transformation of the associated \(3 \times 3\) matrix spectral problem. As applications, abundant intriguing types of nonlinear waves are obtained in zero and nonzero boundary conditions. The dynamical evolution of these nonlinear waves can be well controlled under stimulated Raman scattering and quintic nonlinearity management. Beside that, we also find some novel and interesting conversion phenomena, where a high-order term plays a pivotal role.

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Acknowledgements

This study was funded by National Natural Science Foundation of China (Grant No. 11801367), Natural Science Foundation of Shanghai (Grant No. 17ZR1411600) and Humanities and Social Science Research Planning Fund of the Education Ministry of China (Grant No. 15YJCZH201).

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China

    Cai-qin Song

  2. Department of Applied Mathematics, Shanghai University of International Business and Economics, 1900 Wenxiang Road, Shanghai, 201620, People’s Republic of China

    Hai-qiong Zhao

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  1. Cai-qin Song
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  2. Hai-qiong Zhao
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Correspondence to Hai-qiong Zhao.

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Song, Cq., Zhao, Hq. Dynamics of various waves in nonlinear Schrödinger equation with stimulated Raman scattering and quintic nonlinearity. Nonlinear Dyn 99, 2971–2985 (2020). https://doi.org/10.1007/s11071-020-05478-w

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