Volume 144, Number 4, November 2023
|Number of page(s)
|Mathematical and interdisciplinary physics
|07 December 2023
Nonlocal symmetries, nonlocally related systems, similarity solutions and conservation laws of the Tzitzéica-Dodd-Bullogh equation
National Institute of Technology, Department of Mathematics - Rourkela-769008, India
Received: 28 July 2023
Accepted: 7 November 2023
In this paper, a methodical procedure is utilized for the identification of nonlocal symmetries of the (1+1)-dimensional Tzitzéica-Dodd-Bullogh equation. Firstly, by introducing a set of canonical coordinates corresponding to the local Lie point symmetries, the considered partial differential eq. (PDE) is mapped to an invertibly equivalent PDE system. Furthermore, nonlocal symmetries are obtained from the inverse potential system of the invertibly equivalent PDE system. The exact solutions for the aforementioned PDE are acquired with the help of the extended generalized Kudryashov method corresponding to the admitted symmetries. In addition, the derivation of local conservation laws for the Tzitzéica-Dodd-Bullogh equation is obtained through the multiplier method. Moreover, using a symmetry-based technique and local conservation principles, a complete tree of nonlocally related PDE systems has been constructed.
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