Conservation laws and normal forms of evolution equations

Details Conservation laws and normal forms of evolution equations Conservation laws and normal forms of evolution equations

2010-03-08

arxiv.org/abs/1003.1648v1

Phys.Lett.A374:2210-2217,2010

Physics

Mathematical Physics

16 pages

Scientific paper

10.1016/j.physleta.2010.03.033

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 low-order conservation laws. Examples include Harry Dym equation, Korteweg-de-Vries-type 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.

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