A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves


Wang X., Yue X., Kaabar M. K. , Akbulut A., Kaplan M.

Journal of Ocean Engineering and Science, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1016/j.joes.2022.03.012
  • Journal Name: Journal of Ocean Engineering and Science
  • Journal Indexes: Scopus
  • Keywords: Auxiliary equation method, Beta derivative, Fractional differential equations, Nonlinear equations, Solitary solutions, Symbolic computation
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2022A novel technique, named auxiliary equation method, is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems: the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative. Our solutions were obtained using MAPLE software. This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering. Since a standard equation has not been used as an auxiliary equation for this technique, different and novel solutions are obtained via this technique.