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

Shu Miao (), Zi-Yi Yin, Zi-Rui Li, Chen-Yang Pan and Guang-Mei Wei ()
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Shu Miao: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Zi-Yi Yin: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Zi-Rui Li: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Chen-Yang Pan: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Guang-Mei Wei: School of Mathematical Sciences, Beihang University, Beijing 100191, China

Mathematics, 2024, vol. 12, issue 22, 1-12

Abstract: 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 ( a 1 ( t ) = a 2 ( 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.

Keywords: variable-coefficient GCBS equation; Painlevé analysis; Lie symmetry; conservation law; symbolic computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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