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, cilt.9, sa.5, ss.437-453, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.joes.2022.03.012
  • Dergi Adı: JOURNAL OF OCEAN ENGINEERING AND SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
  • Sayfa Sayıları: ss.437-453
  • Anahtar Kelimeler: Auxiliary equation method, Beta derivative, Fractional differential equations, Nonlinear equations, Solitary solutions, Symbolic computation
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

A 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.