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Exact \(\varvec{N}\)-soliton solutions and dynamics of a new AKNS equation with time-dependent coefficients

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Abstract

Based on the corresponding bilinear forms, we obtain one-, two- and three-soliton solutions of a new AKNS equation with time-dependent coefficients by using Hirota’s bilinear method. From these obtained solutions, uniform formulae of exact N-soliton solutions of the AKNS equation are summarized. It is graphically shown that the dynamical evolutions of such soliton solutions with time-dependent functions of the AKNS equation possess time-varying speeds and amplitudes in the process of propagations.

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Acknowledgments

We would like to express our sincerest thanks to the referee for the valuable suggestions and comments which lead to further improvement of our original manuscript. This work was supported by the Natural Science Foundation of Liaoning Province of China (L2012404), the Ph.D. Start-up Funds of Liaoning Province of China (20141137) and Bohai University (bsqd2013025), the Liaoning BaiQianWan Talents Program (2013921055) and the Natural Science Foundation of China (11371071).

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Zhang, S., Gao, X. Exact \(\varvec{N}\)-soliton solutions and dynamics of a new AKNS equation with time-dependent coefficients. Nonlinear Dyn 83, 1043–1052 (2016). https://doi.org/10.1007/s11071-015-2386-5

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