Modulation stability analysis and solitary wave solutions of nonlinear higher-order Schrödinger dynamical equation with second-order spatiotemporal dispersion

  • Aly R. Seadawy
  • Muhammad Arshad
  • Dianchen Lu
Original Paper


In optical fibers, the higher-order nonlinear Schrödinger (NLS) dynamical equation which describes the beyond the classic slowly varying envelopes and spatiotemporal dispersion of pulses is investigated. By applying the proposed modified extended mapping method, the optical soliton solutions of higher-order NLS dynamical equation with the coefficients of group velocity dispersion, second-order spatiotemporal dispersion and cubic nonlinearity are deduced. The obtained solutions have important applications in applied sciences and engineering. The formation conditions are specified on parameters in which optical solitons can exist for this media. The moments of some constructed solutions are presented graphically which facilitate the researchers to comprehend the physical phenomena of this equation. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are stable and exact. Other such forms of the system arising in sciences and engineering can also be solved by this steadfast, influential and effective method.


Modified extended mapping method Higher-order nonlinear Schrödinger equation Solitons Solitary wave solutions 


02.30.Jr 05.45.Yv 47.10.A? 47.35.+i 47.35.Fg 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTaibah UniversityMedinaSaudi Arabia
  2. 2.Mathematics Department, Faculty of ScienceBeni-Suef UniversityBeni SuefEgypt
  3. 3.Faculty of ScienceJiangsu UniversityZhenjiangPeople’s Republic of China

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