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 …

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 …

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 …

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 …

A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations

SC Anco, PL da Silva, IL Freire - Journal of Mathematical Physics, 2015 - pubs.aip.org
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 …

Symmetry-invariant conservation laws of partial differential equations

SC Anco, AH Kara - European Journal of Applied Mathematics, 2018 - cambridge.org
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 …

Generalization of the double reduction theory

AH Bokhari, AY Al-Dweik, FD Zaman, AH Kara… - Nonlinear Analysis: Real …, 2010 - Elsevier
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 …

Conservation laws and potential symmetries of linear parabolic equations

RO Popovych, M Kunzinger, NM Ivanova - Acta Applicandae …, 2008 - Springer
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 …

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 …

Noether theorem for μ-symmetries

G Cicogna, G Gaeta - Journal of Physics A: Mathematical and …, 2007 - iopscience.iop.org
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 …