Comparing symmetries and conservation laws of nonlinear telegraph equations
نویسنده
چکیده
A comparison is made between the symmetries and conservation laws admitted by nonlinear telegraph NLT systems. Such systems are not variational. Unlike the situation for variational systems where all conservation laws arise from symmetries, there are many NLT systems that admit more conservation laws than symmetries. The results are summarized in a table which includes the numbers of symmetries and conservation laws for each NLT system. It is also indicated when symmetries map conservation laws to other conservation laws. © 2005 American Institute of Physics. DOI: 10.1063/1.1915292
منابع مشابه
On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws
In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.
متن کاملFramework for nonlocally related PDE systems and nonlocal symmetries: extension, simplification, and examples
Any PDE system can be effectively analyzed through consideration of its tree of nonlocally related systems. If a given PDE system has n local conservation laws, then each conservation law yields potential equations and a corresponding nonlocally related potential system. Moreover, from these n conservation laws, one can directly construct 2 − 1 independent nonlocally related systems by consider...
متن کاملFramework for nonlocally related partial differential equation systems and nonlocal symmetries: Extension, simplification, and examples
Any partial differential equation PDE system can be effectively analyzed through consideration of its tree of nonlocally related systems. If a given PDE system has n local conservation laws, then each conservation law yields potential equations and a corresponding nonlocally related potential system. Moreover, from these n conservation laws, one can directly construct 2n−1 independent nonlocall...
متن کاملSymmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation
In this paper Lie point symmetries, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation are investigated. First of all Lie symmetries are obtained by using the general method based on invariance condition of a system of differential equations under a prolonged vector field. Then the structure of symmetry ...
متن کاملConservation laws for nonlinear telegraph equations
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...
متن کامل