Various Composite Periodic Wave Solutions of the Calogero-Bogoyavlenskii-Schiff Equation Based on Bilinear Neural Networks Model
Year: 2026
Type: conference-paper
Abstract: This paper innovatively constructs a novel test function system based on generalized activation functions, successfully addressing the challenge of multi-layer membrane structure solutions for the Calogero-Bogoyavlenskii-Schiff (CBS) equation through the bilinear neural network method (BNNM). Within the classical framework of the bilinear approach, this study introduces the AiryAi function into the construction of auxiliary functions, achieving its mathematical integration with the JacobiCN elliptic function and power functions to form a highly nonlinear hybrid function space. Leveraging the powerful symbolic computation capabilities of the Maple platform, we not only obtain exact analytical solutions ranging from single-layer to four-layer membrane structures, but also reveal the underlying mechanisms of complex dynamical behaviors such as Airy-type lump periodic waves, interaction periodic waves, triple-layer periodic waves and four-layer periodic waves. The research not only enriches the theoretical framework of multi-soliton structures in nonlinear physics, but also opens up new directions in mathematical modeling and intelligent solution methods for complex systems.
Authors: Meiyu Li, Guan-Ting Liu, Yang Wang
Institutions: Inner Mongolia Normal University, Hulunbuir University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7204786348