We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Novel interaction solutions to the (3+1)-dimensional Hirota bilinear equation by bilinear neural network method.
- Authors
Ma, Wenbo; Bilige, Sudao
- Abstract
Solving differential equations is an ancient and very important research topic in theory and practice. The exact analytical solution to differential equations can describe various physical phenomena such as vibration and propagation wave. In this paper, the bilinear neural network method (BNNM), which uses neural network to unify all kinds of classical test function methods, is employed to obtain some new exact analytical solutions of the (3 + 1)-dimensional Hirota bilinear (HB) equation. Based on the Hirota form of the HB equation, we constructed four kinds of new solutions which contain the breather solution, rogue wave solution, breather lump-type soliton solution and the interaction solution between the periodic waves and two-kink wave by introducing a series of test functions in both single-layer and multi-layer neurons such as [4–2–2] and [4–2–3] neural network models. In addition, we compared them to those that had already been published. It is clear that our results are not consistent with those found in these publications. Their corresponding dynamic features are vividly demonstrated in some 3D, contour, x-curves and y-curves plots. The results obtained demonstrate the potential of the proposed methods to solve other nonlinear partial differential equations in fields.
- Subjects
ROGUE waves; NONLINEAR differential equations; PARTIAL differential equations; ARTIFICIAL neural networks; DIFFERENTIAL equations
- Publication
Modern Physics Letters B, 2024, Vol 38, Issue 29, p1
- ISSN
0217-9849
- Publication type
Article
- DOI
10.1142/S0217984924502403