Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 1043–1052 | Cite as

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

Original Paper


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.


Bilinear form Soliton solution  Hirota’s bilinear method AKNS equation with time-dependent coefficients 



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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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsBohai UniversityJinzhouPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsKashgar UniversityKashgarPeople’s Republic of China

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