This book is a sequel to Symmetries and Integration Methods (2002), by George W. Bluman
and Stephen C. Anco. It includes a significant update of the material in the last three …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The direct method for the construction of local conservation laws of partial differential
equations (PDE) is a systematic method applicable to a wide class of PDE systems (S. Anco …

A general method using multipliers for finding the conserved integrals admitted by any given
partial differential equation (PDE) or system of partial differential equations is reviewed and …

For systems of partial differential equations in three spatial dimensions, dynamical
conservation laws holding on volumes, surfaces, and curves, as well as topological …

Symmetry properties of conservation laws of partial differential equations are developed by
using the general method of conservation law multipliers. As main results, simple conditions …

For partial differential equations (PDEs) that have n≥ 2 independent variables and a
symmetry algebra of dimension at least n− 1, an explicit algorithmic method is presented for …

A direct method for the computation of polynomial conservation laws of polynomial systems
of nonlinear partial differential equations (PDEs) in multi‐dimensions is presented. The …

A simple characterization of the action of symmetries on conservation laws of partial
differential equations is studied by using the general method of conservation law multipliers …

A moving frame formulation of non-stretching geometric curve flows in Euclidean space is
used to derive a 1+ 1 dimensional hierarchy of integrable SO (3)-invariant vector models …