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Snakelike similaritons in combined harmonic-lattice potentials with a varying source

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Abstract

We study the dynamics of snakelike similaritons to the nonlinear Schrödinger equation in combined harmonic-lattice potentials with a varying source term. Using the self-similar and Möbius transformations, we construct a large number of analytical solutions which generate many types of novel snakelike similaritons under some constraint conditions, such as the W- and bell-shaped breathing similaritons and the elliptic function solutions. Then, four specific examples of physical interest are considered in details to show the dynamical behaviors of the similaritons. Especially, the compression effect of snakelike similaritons is demonstrated in dispersion-decreasing media with Bessel modulated nonlinearity. We find that the structures of snakelike similaritons can be controlled by tuning the coefficient parameters, the combined harmonic-lattice potentials, and the source term. The stability of the solutions has also been performed by numerical simulations. Our results may have potential applications in the dual-core fiber waveguides and Bose–Einstein condensates in the presence of an inhomogeneous source.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11847103 and the Field Grade Project of HuBei University of Science and Technology under Grant No. 2016-19XB006.

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  1. School of Electronic and Information Engineering, HuBei University of Science and Technology, Xianning, 437100, China

    Jun-Rong He, Wen-Wu Deng & Li Xue

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He, JR., Deng, WW. & Xue, L. Snakelike similaritons in combined harmonic-lattice potentials with a varying source. Nonlinear Dyn 100, 1599–1609 (2020). https://doi.org/10.1007/s11071-020-05584-9

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