47 citations · 85 across the 9 of their papers we have counts for
6 papers · 1 filter
A Symmetry-Based Method for Constructing Nonlocally Related PDE Systems
George W. Bluman, Zhengzheng Yang
Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system…
Conservative parameterization schemes
Alexander Bihlo, George Bluman
Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these mode…
Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws
Stephen C. Anco, George Bluman, Thomas Wolf
An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some…
Connections Between Symmetries and Conservation Laws
George Bluman
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 M…
Direct construction method for conservation laws of partial differential equations. Part II: General treatment
Stephen C. Anco, George Bluman
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservatio…
Direct construction method for conservation laws of partial differential equations. Part I: Examples of conservation law classifications
Stephen C. Anco, George Bluman
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The…