Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction o...

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inho...

Abstract The elastic wave propagation in inelastic media gives rise to non-linear equation. We study such a nonlinear two dimensions using Murnaghan model. Lie symmetries, invariant exact solutions and conservation laws the Noether theorem have been found. equation with damping term has dealt partial approach.

This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit ana...

Abstract In this paper, by using the Lie symmetry analysis, all of geometric vector fields $(3+1)$ (3+1) -Burgers system are obtained. We find 1, 2, and 3-dimensional optimal Burger then applying reduce order system. Also nonclassical symmetrie...