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Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation

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Abstract

A novel complex nonlinear wave equation was recently found by Mukherjee and Kundu (Phys. Lett. A 383:985–990, 2019) and shown that it possesses the first-order rogue waves and accelerated one-soliton solutions. In this paper, higher-order rogue wave solutions with multi-parameters of the novel complex nonlinear wave equation are derived by a symbolic computation approach. Nonlinear dynamics of the first- and second-order rogue wave solutions, localized in space–time and richer due to the presence of free parameters, are investigated in detail. In particular, a complete classification of the first-order rogue wave is given by the free parameters. With the help of the contour line method, some localization characters of the first-order rogue wave solution are analyzed. Moreover, the novel equation also allows some periodic wave and accelerated periodic wave solutions expressed by Jacobi elliptical functions.

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Acknowledgements

The authors deeply appreciate the anonymous reviewers for their helpful and constructive suggestions, which can help improve this paper further. This work is supported by the National Natural Science Foundation of China (under Grant Nos. 11861050, 11261037) and Caoyuan Yingcai Program of Inner Mongolia Autonomous Region (under Grant No. CYYC2011050).

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Correspondence to Zhaqilao.

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Zhaqilao Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation. Nonlinear Dyn (2020) doi:10.1007/s11071-019-05458-9

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Keywords

  • Rogue wave solution
  • Periodic wave solution
  • Symbolic computation approach
  • Novel complex nonlinear wave equation