Nonlocal symmetries, nonlocally related systems, similarity solutions and conservation laws of Tzitzeica-Dodd-Bullogh equation

Abstract In this paper, a methodical procedure is proposed for the identification of nonlocal symmetries
of the (1+1)-dimensional Tzitzeica-Dodd-Bullogh equation. Firstly, by introducing a set
of canonical coordinates corresponding to the local Lie point symmetries, the considered partial
differential equation (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 point symmetries. In
addition, using a symmetry-based technique and local conservation principles, a complete tree of
nonlocally associated PDE systems has been constructed. Additionally, the derivation of local
conservation laws for the Tzitzeica-Dodd-Bullogh equation is obtained through the multiplier
method.