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Theoretical and numerical investigations on solitary wave solutions of Gardner equation

  • Turgut AkEmail author
  • Houria Triki
  • Sharanjeet Dhawan
  • Kutsi S. Erduran
Regular Article

Abstract.

This paper formulates new hyperbolic functions ansatze to construct exact solitary wave solutions of the Gardner (combined KdV-mKdV) equation and a finite element approach for the numerical solutions. A novel class of exact solitary wave solutions is derived. The conditions on the physical parameters for the existence of the obtained structures are also presented. Accuracy of the proposed numerical scheme is assessed in terms of L2 and \(L_{\infty}\) error norms. Numerical experiments demonstrate the accuracy and robustness of the method which can be further used for solving other nonlinear problems.

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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.Armutlu Vocational SchoolYalova UniversityYalovaTurkey
  2. 2.Radiation Physics Laboratory, Department of Physics, Faculty of SciencesBadji Mokhtar UniversityAnnabaAlgeria
  3. 3.Department of MathematicsCentral University of HaryanaHaryanaIndia
  4. 4.Department of Civil EngineeringNigde Omer Halisdemir UniversityNigdeTurkey

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