Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

The calculus of variations has a long history of interaction with other branches of
mathematics such as geometry and differential equations, and with physics, particularly …

The fundamental relation between Lie-Bäcklund symmetry generators andconservation laws
of an arbitrary differential equation is derived without regardto a Lagrangian formulation of …

This Letter presents an algorithm to obtain all local conservation laws for any system of field
equations. The algorithm uses a formula which directly generates the conservation laws and …

Conservation laws are formulated for systems of differential equations by using symmetries
and adjoint symmetries, and an application to systems of evolution equations is made …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

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 …

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 …

The motivation for the present book originated in the quest to understand wavewave
interactions in magnetohydrodynamics (MHD) in a non-uniform background flow (this …

Our research focuses on a fourth-order partial differential equation (PDE) that arises from the
Timoshenko model for beams. This PDE pertains to situations where the elastic moduli …