Abstract In this paper, a Lie symmetry method is used for the nonlinear generalized Camassa–Holm equation and as result reduction of order computing conservation laws are presented. Furthermore, μ -symmetry -conservation obtained.

In this paper, a time-fractional derivative nonlinear Schrödinger equation involving the Riemann–Liouville fractional is investigated. We first perform Lie symmetry analysis of equation, and then derive reduced equations under admitted optimal-symmetry system. Moreover, with invariant subspace method, several exact solutions for their figures are presented. Finally, new conservation theorem app...

We characterize the family of second order potential differential systems, with n degrees of freedom, via their symmetries. Firstly, we calculate explicitly the equivalence Lie algebra and the weak equivalence Lie algebra. It is shown that the equivalence Lie algebra has the dimension n + 4 + n(n− 1) 2 whereas the weak equivalence Lie algebra is infinitedimensional. The later contains strictly ...

Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various ...

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper [8]) that for some special choices of the reparametrisation parameter ǫ, one can obtain space-space noncommuting structures which are Lie-algebraic in for...

Automorphic Lie Algebras are interesting because of their fundamental nature and their role in our understanding of symmetry. Particularly crucial is their description and classification as it allows us to understand and apply them in different contexts, from mathematics to physical sciences. While the problem of classification of Automorphic Lie Algebras with dihedral symmetry was already cons...

The recent systematic study by Janocha et al. [1] to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two ...