Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether’s theorem
نویسنده
چکیده
The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of the linearized equation due to the Noether’s theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and the conservation laws that are explicitly expressed through the variables of the nonlinear equations are derived.
منابع مشابه
Derivation of conservation laws from nonlocal symmetries of differential equations
An identity is derived which yields a correspondence between symmetries and conservation laws for self-adjoint differential equations. This identity does not rely on use of a Lagrangian as needed to obtain conservation laws by Noether’s theorem. Moreover, unlike Noether’s theorem, which can only generate conservation laws from local symmetries, the derived identity generates conservation laws f...
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 کاملOn 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 کاملConnections Between Symmetries and Conservation Laws
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether’s theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for any given system of differential equations. This method yields the multipliers for conservation laws as well as an integral formula for corresponding conser...
متن کاملOn conservation integrals in micropolar elasticity
Two conservation laws of nonlinear micropolar elasticity (Jk = 0 and Lk = 0) are derived within the framework of Noether’s theorem on invariant variational principles, thereby extending the earlier authors’ results from the couple stress elasticity. Two non-conserved M -type integrals of linear micropolar elasticity are then derived and their values discussed. The comparison with related work i...
متن کامل