Seminar talk, 22 February 2023

From Geometry of Differential Equations
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Speaker: Alexey Samokhin

Title: On perturbations retaining conservation laws of differential equations

The talk deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay. These rates are described by the simple law using the conservation laws' generating functions and the added term. Yet some perturbation may retain a specific quantity(s), such as energy, momentum and other physically important characteristics of solutions. We introduce a procedure for finding such perturbations and demonstrate it by examples including the KdV-Burgers equation and a system from magnetodynamics.