Direct construction method for conservation laws of partial differential equations Part II: General treatment

By Stephen C. Anco, George Bluman. European journal of applied mathematics, 2001

431 citations recorded by the source corpus.

This paper gives a general treatment and proof of the direct conservation law method presented in Part I (see Anco & Bluman [3]). In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential equations expressed in a standard Cauchy-Kovalevskaya form. A summary of the general method and its effective computational implementation is also given.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d1d305fc4e5b0a54f95de529b71dc1f2a5f64441

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Abdul Hamid Kara
2. Fazal Mahmood Mahomed
3. Alexei F. Cheviakov
4. George Bluman

In Statistical and Nonlinear Physics

1. Fazal Mahmood Mahomed
2. Abdul Hamid Kara
3. Alexei F. Cheviakov
4. Ahmad Y. Al-Dweik
5. Fiazud Din Zaman
6. Ashfaque H. Bokhari
7. George Bluman

Citations in the corpus

• Framework for potential systems and nonlocal symmetries: Algorithmic approach (2005, methodology): “In general, for any system of DEs the algorithmic direct construction method [11, 12] yields its conservation laws.”
• Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians (2006, methodology): “The paper [ 11 ] uses the latter approach and gives an algorithm 368 A. H. Kara and F. M. Mahomed”
• Double reduction of a nonlinear (2+1) wave equation via conservation laws (2011, background): “Other situations have been investigated in [1,11] and [9].”