Nonlinear Dynamics

, Volume 98, Issue 2, pp 1491–1500 | Cite as

Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation

  • Xue Guan
  • Wenjun LiuEmail author
  • Qin Zhou
  • Anjan Biswas
Original Paper


Darboux transformation is an efficient method for solving different nonlinear partial differential equations. In this paper, on the basis of a Lie super-algebras, a generalized super-NLS-mKdV equation is solved by the Darboux transformation. The analytic solutions are presented with the help of symbolic computation. Besides, two special cases are given to make the solution intuitive. Dynamic properties of solitons are also discussed.


Solitons Lie super-algebra Darboux transformation Analytic solution Super-NLS-mKdV equation 



The work of Wenjun Liu was supported by the National Natural Science Foundation of China (Grant Nos. 11674036 and 11875008), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833ZK08) and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant No. IPOC2017ZZ05).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingPeople’s Republic of China
  2. 2.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanPeople’s Republic of China
  3. 3.Department of Physics, Chemistry and MathematicsAlabama A & M UniversityNormalUSA
  4. 4.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  5. 5.Department of Mathematics and StatisticsTshwane University of TechnologyPretoriaSouth Africa

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