A Reliable Study of New Nonlinear Equation: Two-Mode Kuramoto–Sivashinsky

  • H. M. Jaradat
  • Marwan Alquran
  • Muhammed I. Syam
Original Paper

Abstract

In this letter, we use the sense made by Korsunsky (Phys Lett A 185:174–176, 1994 ) to establish a new nonlinear equation called the two-mode Kuramoto–Sivashinsky (TMKS). A finite series in terms of the Tanh function is proposed to be a candidate solution to this new model. Also, we study possible solutions of TMKS by means of the modified simplified bilinear method where a new Cole-Hopf transformation is considered. The new model describes the propagation of two different wave modes simultaneously.

Keywords

Two-mode Kuramoto–Sivashinsky Solitons Tanh-Expansion method Simplified Bilinear method 

Mathematics Subject Classification

35C08 74J35 

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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  • H. M. Jaradat
    • 1
  • Marwan Alquran
    • 2
  • Muhammed I. Syam
    • 3
  1. 1.Department of MathematicsAl al-Bayt UniversityMafraqJordan
  2. 2.Department of Mathematics and StatisticsJordan University of Science and TechnologyIrbidJordan
  3. 3.Department of Mathematical SciencesUAE UniversityAl-AinUnited Arab Emirates

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