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Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation

  • Rehab M. El-Shiekh ORCID logo EMAIL logo und Mahmoud Gaballah
Veröffentlicht/Copyright: 10. August 2020
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International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 21 Heft 7-8

Abstract

In this paper, the generalized nonlinear Schrödinger equation with variable coefficients (gvcNLSE) arising in optical fiber is solved by using two different techniques the trail equation method and direct integration method. Many different new types of wave solutions like Jacobi, periodic and soliton wave solutions are obtained. From this study we have concluded that the direct integration method is more easy and straightforward than the trail equation method. As an application in optic fibers the propagation of the frequency modulated optical soliton is discussed and we have deduced that it's propagation shape is affected with the different values of both the amplification increment and the group velocity (GVD).

Keywords: bright and dark solitons; direct reduction method; generalized variable coefficients nonlinear Schrödinger equation; multiply wave solutions; trail equation method
Corresponding author: Rehab M. El-Shiekh, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt; and College of Business Administration in Majmaah, Majmaah University 11952, Kingdom of Saudi Arabia. E-mail: ,

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This research was funded by Majmaah University.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2019-02-08
Accepted: 2020-03-25
Published Online: 2020-08-10
Published in Print: 2020-11-18

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. ANFIS based system identification of underactuated systems
  4. The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
  5. A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
  6. Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
  7. A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
  8. Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
  9. Integrodifference master equation describing actively growing blood vessels in angiogenesis
  10. On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
  11. Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
  12. Lie symmetries and singularity analysis for generalized shallow-water equations
  13. Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
  14. Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
  15. Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
  16. The barotropic Rossby waves with topography on the earth’s δ-surface
  17. Synchronization control between discrete uncertain networks with different topologies
  18. Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
  19. Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
  20. A parallel hybrid implementation of the 2D acoustic wave equation
  21. Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
  22. Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
  23. Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber
https://doi.org/10.1515/ijnsns-2019-0054
Schlagwörter für diesen Artikel
bright and dark solitons; direct reduction method; generalized variable coefficients nonlinear Schrödinger equation; multiply wave solutions; trail equation method

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. ANFIS based system identification of underactuated systems
  4. The dynamical behavior of mixed type lump solutions on the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation
  5. A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation
  6. Bright and dark optical solitons for the generalized variable coefficients nonlinear Schrödinger equation
  7. A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations
  8. Global dissipativity and exponential synchronization of mixed time-varying delays neural networks with discontinuous activations
  9. Integrodifference master equation describing actively growing blood vessels in angiogenesis
  10. On the behaviors of rough multilinear fractional integral and multi-sublinear fractional maximal operators both on product Lp and weighted Lp spaces
  11. Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps
  12. Lie symmetries and singularity analysis for generalized shallow-water equations
  13. Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system
  14. Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals
  15. Lie symmetry analysis and similarity solutions for the Jimbo – Miwa equation and generalisations
  16. The barotropic Rossby waves with topography on the earth’s δ-surface
  17. Synchronization control between discrete uncertain networks with different topologies
  18. Boundary shape functions methods for solving the nonlinear singularly perturbed problems with Robin boundary conditions
  19. Global exponential stability analysis of anti-periodic solutions of discontinuous bidirectional associative memory (BAM) neural networks with time-varying delays
  20. A parallel hybrid implementation of the 2D acoustic wave equation
  21. Approximate controllability of fractional stochastic evolution equations with nonlocal conditions
  22. Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws
  23. Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber
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