A Novel Neural Network-Based Symbolic Approach for Shallow-Water Waves with Surface Tension


González-Gaxiola O., Hart-Simmons M., Ahmed H. M., Biswas A.

Fluids, cilt.11, sa.4, 2026 (ESCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 4
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3390/fluids11040100
  • Dergi Adı: Fluids
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: Boussinesq equation, Kudryashov R-function, neural networks, symbolic computation
  • Karadeniz Teknik Üniversitesi Adresli: Hayır

Özet

This paper examines the sixth-order generalized Boussinesq equation, which describes the dynamics of shallow-water waves, including the effects of surface tension. The study introduces Kudryashov’s R-function neural network approach for the first time, aiming to provide exact solutions to the nonlinear differential equation that represents the mathematical model of the sixth-order generalized Boussinesq equation. This technique incorporates the solutions of a nonlinear differential equation into neural networks, using them as an activation function within the hidden layer. In line with previous research on this topic, two categories of solutions are derived: solitary wave and shock wave solutions. Additionally, this paper includes 3D and 2D graphs to visually represent the solutions obtained.