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More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics

  • Nadia Cheemaa
  • Aly R. SeadawyEmail author
  • Sheng Chen
Regular Article

Abstract.

In this article we analytically studied the complex nonlinear Schrödinger equation with Kerr law nonlinearity using the auxiliary equation mapping method, as a result, we found a series of more general and new families of exact solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies, nonlinear optics and many other fields. The calculations demonstrate that this method is more reliable, straightforward and effective to analytically study other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We have also expressed our solutions graphically with the help of Mathematica 10.4 to physically understand the behavior of different shapes of solutions including kink-type, anti-kink-type, half-bright and dark solitons.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of Mathematics, Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia
  3. 3.Mathematics Department, Faculty of ScienceBeni-Suef UniversityBeni SuefEgypt

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