Novel multiple soliton and front wave solutions for the 3D-Vakhnenko-Parkes equation

Sağlam Özkan Y., Yaşar E., Osman M. S.

MODERN PHYSICS LETTERS B, vol.36, no.09, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 09
  • Publication Date: 2022
  • Doi Number: 10.1142/s0217984922500038
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, INSPEC, zbMATH
  • Keywords: The multiple exp-function method, multiple soliton solutions, linear superposition principle, Vakhnenko-Parkes equation, FOKAS-LENELLS EQUATION
  • Bursa Uludag University Affiliated: Yes


The multiple exp-function technique, as an extension to Hirota's perturbation algorithm, is employed to find N-soliton solutions of the 3D Vakhnenko-Parkes (3D-VP) equation. This is a straightforward and effective alternative method. Consequently, one- two- and three-soliton solutions besides the front wave solutions and their wave numbers are obtained, which are completely distinct from the other published literature. 3D and density plots were investigated via the help of the Maple package program by suitably choosing the free parameters in the solutions. Further, the physical meaning for these solutions is clarified. We mention that the propagation of high-frequency waves in a relaxing medium can be investigated by discussing the dynamical behavior of the obtained solutions for the 3D-VP equation.