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Soliton Solutions and Other Solutions for Kundu–Eckhaus Equation with Quintic Nonlinearity and Raman Effect Using the Improved Modified Extended Tanh-Function Method

Author

Listed:
  • Karim K. Ahmed

    (Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Abbassia, Cairo P.O. Box 11517, Egypt
    Department of Mathematics, Faculty of Basic Sciences, German University in Cairo, Cairo P.O. Box 11835, Egypt)

  • Niveen M. Badra

    (Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Abbassia, Cairo P.O. Box 11517, Egypt)

  • Hamdy M. Ahmed

    (Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo P.O. Box 11837, Egypt)

  • Wafaa B. Rabie

    (Department of Basic Sciences, Higher Institute of Engineering and Technology, Menoufia P.O. Box 32821, Egypt)

Abstract

Our paper studies the optical solitons for the Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, many soliton solutions can be obtained such as bright soliton solutions, dark soliton solutions, and the singular soliton solution. In addition, we can obtain various types of solutions, namely, singular periodic solutions, exponential solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some selected solutions are illustrated graphically to show the physical nature and the characteristics of the obtained solutions.

Suggested Citation

  • Karim K. Ahmed & Niveen M. Badra & Hamdy M. Ahmed & Wafaa B. Rabie, 2022. "Soliton Solutions and Other Solutions for Kundu–Eckhaus Equation with Quintic Nonlinearity and Raman Effect Using the Improved Modified Extended Tanh-Function Method," Mathematics, MDPI, vol. 10(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4203-:d:968486
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