On the Rosenau equation: Lie symmetries, periodic solutions and solitary wave dynamics


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Demirci A., Hasanoğlu Y., Muslu G. M., Özemir C.

Wave Motion, vol.109, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 109
  • Publication Date: 2022
  • Doi Number: 10.1016/j.wavemoti.2021.102848
  • Journal Name: Wave Motion
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Geobase, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Rosenau equation, Solitary waves, Lie symmetries, Periodic solutions, Petviashvili method, Fourier pseudo-spectral method
  • Istanbul Technical University Affiliated: Yes

Abstract

© 2021 Elsevier B.V.In this paper, we first consider the Rosenau equation with the quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of the equation to ODEs, and find periodic analytical solutions in terms of elliptic functions. Then, considering a general power-type nonlinearity, we prove the non-existence of solitary waves for some parameters using Pohozaev type identities. The Fourier pseudo-spectral method is proposed for the Rosenau equation with this single power type nonlinearity. In order to investigate the solitary wave dynamics, we generate the initial solitary wave profile by using the Petviashvili's method. Then the evolution of the single solitary wave and overtaking collision of solitary waves are investigated by various numerical experiments.