Seminar talk, 31 March 2010
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Speaker: Joseph Krasil'shchik
Title: Conservation laws and normal forms of evolution equations
Abstract:
After the paper by Roman Popovych and Artur Sergyeyev by the same title, Phys. Lett. A (2010), arXiv:1003.1648
Summary of the paper: "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."