Generalization of Noether's theorem in modern form to non-variational partial differential equations
SC Anco - Recent progress and modern challenges in applied …, 2017 - Springer
A general method using multipliers for finding the conserved integrals admitted by any given
partial differential equation (PDE) or system of partial differential equations is reviewed and …
partial differential equation (PDE) or system of partial differential equations is reviewed and …
Symmetry properties of conservation laws
SC Anco - International Journal of Modern Physics B, 2016 - World Scientific
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 …
using the general method of conservation law multipliers. As main results, simple conditions …
Symmetry multi-reduction method for partial differential equations with conservation laws
SC Anco, ML Gandarias - … in Nonlinear Science and Numerical Simulation, 2020 - Elsevier
For partial differential equations (PDEs) that have n≥ 2 independent variables and a
symmetry algebra of dimension at least n− 1, an explicit algorithmic method is presented for …
symmetry algebra of dimension at least n− 1, an explicit algorithmic method is presented for …
On the Lie algebras, generalized symmetries and Darboux transformations of the fifth-order evolution equations in shallow water
S Tian, Y Zhang, B Feng, H Zhang - Chinese Annals of Mathematics …, 2015 - Springer
By considering the one-dimensional model for describing long, small amplitude waves in
shallow water, a generalized fifth-order evolution equation named the Olver water wave …
shallow water, a generalized fifth-order evolution equation named the Olver water wave …
A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations
A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov
equations that describe breaking waves is introduced. A classification of low-order …
equations that describe breaking waves is introduced. A classification of low-order …
Symmetry-invariant conservation laws of partial differential equations
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 …
differential equations is studied by using the general method of conservation law multipliers …
Generalization of the double reduction theory
In a recent work Sjöberg (2007, 2008)[1, 2] remarked that generalization of the double
reduction theory to partial differential equations of higher dimensions is still an open …
reduction theory to partial differential equations of higher dimensions is still an open …
Conservation laws and potential symmetries of linear parabolic equations
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 …
the class of linear (1+ 1)-dimensional second-order parabolic equations. The group …
Symmetry reductions, exact solutions, and conservation laws of the generalized Zakharov equations
E Buhe, GW Bluman - Journal of Mathematical Physics, 2015 - pubs.aip.org
In this paper, the generalized Zakharov equations, which describe interactions between high-
and low-frequency waves in plasma physics are studied from the perspective of Lie …
and low-frequency waves in plasma physics are studied from the perspective of Lie …
Noether theorem for μ-symmetries
We give a version of Noether theorem adapted to the framework of μ-symmetries; this
extends to such case recent work by Muriel, Romero and Olver in the framework of λ …
extends to such case recent work by Muriel, Romero and Olver in the framework of λ …