Abstract
This paper applies the direct construction method, symmetry/adjoint symmetry pair method (SA method), symmetry action on a known conservation law method, Ibragimov’s conservation theorem (which always yields the same results as the SA method) and a recursion formula to calculate several conservation laws for nonlinear telegraph systems. In addition, a comparison is made between these methods for conservation laws admitted by nonlinear telegraph systems.
Highlights
Conservation laws are essential in many fields of applications
We have summarized how to calculate conservation laws from the direct construction method, SA method, symmetry action on a known conservation law method, Ibragimov’s conservation theorem and a recursion formula when a symmetry transformation is admitted by a given partial differential equations (PDEs)
The direct method yields all conservation laws resulting from the corresponding multipliers for a PDE system written in Cauchy–Kovalevskaya form
Summary
Conservation laws are essential in many fields of applications. In particular, they are important in studying the properties of solutions, integrability and in the development of numerical solutions for partial differential equations (PDEs). In Ibragimov’s conservation theorem [11], a general formula on conservation laws for arbitrary PDEs is stated by combining the Lie symmetry generators and adjoint equations with formal Lagrangians.
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