An effective algorithmic method is presented for finding the local conservation laws for
partial differential equations with any number of independent and dependent variables. The …

This paper gives a general treatment and proof of the direct conservation law method
presented in Part I (see Anco & Bluman [3]). In particular, the treatment here applies to …

The paper compares computational aspects of four approaches to compute conservation
laws of single Differential Equations (DEs) or systems of them, ODEs and PDEs. The only …

For a given second-order ordinary differential equation (ODE), several relationships among
first integrals, integrating factors and λ-symmetries are studied. The knowledge of a λ …

Conservation law plays a vital role in the study of nonlinear evolution equations, particularly
with regard to integrability, linearization and constants of motion. In the present paper, it is …

In this paper, we consider a generalized second-order nonlinear ordinary differential
equation (ODE) of the form x ̈+(k 1 x q+ k 2) x ̇+ k 3 x 2 q+ 1+ k 4 x q+ 1+ λ 1 x= 0⁠, where …

Different approaches to construct first integrals for ordinary differential equations and
systems of ordinary differential equations are studied here. These approaches can be …

This paper describes a new symmetry-based approach to solving a given ordinary
difference equation. By studying the local structure of the set of solutions, we derive a …

The Zakharov–Kuznetsov (ZK) equation is extensively investigated in this study. This
equation is a two-dimensional (2D) generalization of the well-known Korteweg–de Vries …

Two formulas are introduced to directly obtain new conservation laws for any system of
partial differential equations from a known conservation law and admitted symmetries. The …