Akademik Veri Yönetim Sistemi
Khayyam Journal of Mathematics, cilt.10, sa.2, ss.228-248, 2024 (Scopus)
Abstract. 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.