Invariance properties, exact and explicit solutions of time-fractional Gear-Grimshaw model

San S., Koc B.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.19, sa.11, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 11
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s0219887822501729
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Fractional partial differential equations, Lie symmetry, explicit solutions, Sine-Gordon expansion method, LIE SYMMETRY ANALYSIS, DIFFERENTIAL-EQUATIONS, WAVE SOLUTIONS, SERIES
  • Eskişehir Osmangazi Üniversitesi Adresli: Evet

Özet

In this study, we consider a time-fractional shallow water wave model which was introduced by Gear and Grimshaw. This model represents the dynamics of two-layered shallow water waves in oceans and rivers. Also it covers many shallow water wave models with special values taken to parameters. By performing the group invariant analysis approach for the governing system with Riemann-Liouville derivative, symmetry generators were found. Similarity reduction was constructed by Erdelyi-Kober sense. In addition, by adapting the Sine-Gordon expansion method, we find some exact traveling wave solutions. Furthermore, explicit solutions in form of power series are examined via the residual power series method. Exact and approximate solutions are compared for some alpha values and these are given as tables.