A new (3+1) dimensional Hirota bilinear equation: Painlavé integrability, Lie symmetry analysis, and conservation laws. Issue 1 (31st December 2022)

• Record Type: Journal Article
• Authors: Günhan Ay, Nursena; Yaşar, Emrullah
• Is Part Of: Journal of Taibah University for science. Volume 16:Issue 1(2022)
• Page Start: 1287
• Page End: 1297
• Publication Date: 2022-12-31
• Subjects: Painlevé analysis -- Lie symmetry -- group-invariant solutions -- conservation laws; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2022.2160538
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : This study's subject is a (3 + 1) dimensional new Hirota bilinear (NHB) equation that appears in the theory of shallow water waves. We investigate how particular dispersive waves behave in an NHB equation. In this regard, we first test the Painlavé integrability using the WTC-Kruskal method and second perform Lie point symmetry analysis on NHB. The algorithm outputs the Lie algebra, the symmetry reductions, and group invariant solutions. Using Lie point symmetries, NHB transforms into an ordinary differential equation. The integration architectures to solve this equation are the Bernoulli sub-ODE, 1/ G ′, and modified Kudryashov methods. We plot their graphs and observe how the solutions behaved in understanding the physical phenomenon. Additionally, we discuss the model utilizing nonlinear self-adjointness and Ibragimov's approach to generate conservation laws for each Lie symmetry generator.