Conservation laws and normal forms of evolution equations
Abstract
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two loworder conservation laws. Examples include Harry Dym equation, Kortewegde Vriestype equations, and Schwarzian KdV equation. It is also shown that for linear evolution equations all their conservation laws are (modulo trivial conserved vectors) at most quadratic in the dependent variable and its derivatives.
 Publication:

Physics Letters A
 Pub Date:
 May 2010
 DOI:
 10.1016/j.physleta.2010.03.033
 arXiv:
 arXiv:1003.1648
 Bibcode:
 2010PhLA..374.2210P
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 35K55 (Primary);
 35A30;
 37K05;
 37K35 (Secondary)
 EPrint:
 16 pages