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Novel wave structures in the two-dimensional cubic–quintic nonlinear Schrödinger equation with space-modulated potential and nonlinearities

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Abstract

We investigate the two-dimensional cubic–quintic nonlinear Schrödinger (CQNLS) equation with space-modulated potential and nonlinearities, which describes the nonlinear wave interactions in nonlinear optics and Bose–Einstein condensates. We use the modified conformal mapping, the Cauchy–Riemann equation, and its extension to present many types of new wave structures of this CQNLS model for different external potentials and nonlinearities, which exhibit bright-like and dark-like solitons, vortex solitons, and other types of wave solutions. Moreover, we also analyze the velocity fields and transverse power-flow or Poynting vectors related to the obtained wave solutions and find the direct relationships between the velocity fields and transverse power-flow or Poynting vectors.

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Acknowledgments

The author would like to thank the referees for their valuable suggestions. This work was partially supported by the NSFC (No. 61178091).

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  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, 100190, China

    Zhenya Yan

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  1. Zhenya Yan
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Correspondence to Zhenya Yan.

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Yan, Z. Novel wave structures in the two-dimensional cubic–quintic nonlinear Schrödinger equation with space-modulated potential and nonlinearities. Nonlinear Dyn 82, 119–129 (2015). https://doi.org/10.1007/s11071-015-2143-9

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