An Analysis of the Lie Symmetry and Conservation Law of a Variable-Coefficient Generalized Calogero–Bogoyavlenskii–Schiff Equation in Nonlinear Optics and Plasma Physics

In this paper, the symmetries and conservation laws of a variable-coefficient generalized Calogero–Bogoyavlenskii–Schiff (vcGCBS) equation are investigated by modeling the propagation of long waves in nonlinear optics, fluid dynamics, and plasma physics. A Painlevé analysis is applied using the Krus...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-11, Vol.12 (22), p.3619
Main Authors: Miao, Shu, Yin, Zi-Yi, Li, Zi-Rui, Pan, Chen-Yang, Wei, Guang-Mei
Format: Article
Language:English
Subjects:
Algebra
conservation law
Conservation laws
Environmental law
Fluid dynamics
Lie groups
Lie symmetry
Nonlinear dynamics
Nonlinear optics
Ordinary differential equations
Painlevé analysis
Partial differential equations
Physics
Plasma physics
symbolic computation
Symmetry
variable-coefficient GCBS equation
Wave propagation
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Summary:In this paper, the symmetries and conservation laws of a variable-coefficient generalized Calogero–Bogoyavlenskii–Schiff (vcGCBS) equation are investigated by modeling the propagation of long waves in nonlinear optics, fluid dynamics, and plasma physics. A Painlevé analysis is applied using the Kruskal-simplified form of the Weiss–Tabor–Carnevale (WTC) method, which shows that the vcGCBS equation does not possess the Painlevé property. Under the compatibility condition (a1(t)=a2(t)), infinitesimal generators and a symmetry analysis are presented via the symbolic computation program designed. With the Lagrangian, the adjoint equation is analyzed, and the vcGCBS equation is shown to possess nonlinear self-adjointness. Based on its nonlinear self-adjointness, conservation laws for the vcGCBS equation are derived by means of Ibragimov’s conservation theorem for each Lie symmetry.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12223619