A method based on innnite parameter conservation laws is described to factor linear differential operators out of nonlinear partial diierential equations (PDEs) or out of diierential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (system) if that is possible. Innnite parameter conservation laws can be computed, for example, with a computer alg...

Many physical processes are described by conservative quasilinear systems of equations that admit a supplementary independent conservation law. A typical example is the equations of incompressible fluid dynamics. If for basic equations the conservation laws of the momentum and the volume are chosen then the conservation law of the energy is an additional conservation law. In the present paper a...

A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the correspond...

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravita...

The paper presents a connection between Lie symmetries and conservation laws for the 2D Ricci flow model.The procedure starts by obtaining a set of multipliers which generates conservation laws.Then, taking into account the most general form of multiplier and making use of a relation which connects Lie symmetries and conservation laws for any dynamical system, one determines associated symmetry...

In her famous paper [14] Emmy Noether proved that each Noether symmetry associated with a Lagrangian generates a conservation law. (Modern treatment of relationship between components of Noether conserved vector and Lie–Bäcklund operators which are Noether symmetries was adduced in [10,18]. Kara et al [12,13] constructed conservation laws of some classes of PDEs with two independent variables u...

Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy soluti...

We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible transformations, the notion of normalized classes of differential equations and the adjoint variational principle. All possible potential conservation laws are d...

Several results about the stability of waves in systems of conservation/balance laws, disseminated in the litterature, obey to a common rule. The linear/spectral stability of the microscopic pattern (the internal structure of the wave) implies the well-posedness of a macroscopic Cauchy problem for an other system of conservation laws. The latter is often obtained by retaining only the conservat...

Using the Spencer-Goldschmidt version of the Cartan-Kähler theorem, we give conditions for (local) existence of conservation laws for analytical quasi-linear systems of two independent variables. This result is applied to characterize the recursion operator (in the sense of Magri) of completely integrable systems. Introduction A conservation law for a (1-1) tensor field h on a manifold M is a 1...