BILINEAR NEURAL NETWORK METHOD FOR OBTAINING THE EXACT ANALYTICAL SOLUTIONS TO NONLINEAR EVOLUTION EQUATIONS AND ITS APPLICATION TO KdV EQUATION
Khayyam Journal of Mathematics, cilt.10, sa.2, ss.228-248, 2024 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 10 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.22034/kjm.2024.396918.2865
- Dergi Adı: Khayyam Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.228-248
- Anahtar Kelimeler: Hirota bilinear form, The bilinear neural network method, the KdV equation, Traveling wave solution
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
Most conventional test functions for solving nonlinear partial differential equations can be built using a single and double hidden layer neural network model via the bilinear neural network method, as is well known. The neural network test function model for the KdV equation is extended to the”2 − 3 − 1” and”2 − 2 − 2 − 1” models in this research. To find analytical solutions to the KdV equation, some new test functions are developed by giving some unique activation functions. By choosing some parameters, lump wave, bright, kink soliton solutions and various soliton solutions are generated. The relationship between the frequency velocity of the wave and the wave intensity as well as the stability analysis of the obtained solutions are studied which provide us a fresh perspective on how to explore the model in detail. The dynamical features of these waves are shown using two-dimensional graphs, three-dimensional graphs and contour plots.