Application of multivariate bilinear neural network method to fractional partial differential equations

Autor: Jian-Guo Liu, Wen-Hui Zhu, Ya-Kui Wu, Guo-Hua Jin
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Results in Physics, Vol 47, Iss , Pp 106341- (2023)
Druh dokumentu: article
ISSN: 2211-3797
DOI: 10.1016/j.rinp.2023.106341
Popis: In this work, a multivariate bilinear neural network method is proposed to seek more exact analytical solutions of nonlinear partial differential equations. As an example, the (2+1)-dimensional fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko equation is investigated via selecting the 3-2-2-1, 3-2-3-1 and 3-3-2-1 models, respectively. The exact analytical solutions with several arbitrary activation functions are derived and the dynamics properties are shown in some three-dimensional and density maps by choosing different activation functions.
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