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New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity

  • M. S. OsmanEmail author
  • Behzad Ghanbari
  • J. A. T. Machado
Regular Article
  • 20 Downloads

Abstract.

A variety of new complex waves representing solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity is investigated. Two different approaches are used, namely the generalized exponential function and the unified methods. Complex periodic, solitary, soliton, and elliptic wave solutions of phenomena that occur in nonlinear optics or in plasma physics are obtained. The physical meaning of the geometrical structures for some solutions is discussed for different choices of the free parameters. It is shown that the proposed methods lead to powerful mathematical tools for obtaining the exact traveling wave solutions of complex nonlinear evolution equations.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt
  2. 2.Department of MathematicsDuba University College, University of TabukTabukSaudi Arabia
  3. 3.Department of Engineering ScienceKermanshah University of TechnologyKermanshahIran
  4. 4.Institute of Engineering, Polytechnic of PortoDepartment of Electrical EngineeringPortoPortugal

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