Seminar talk, 22 February 2023: Difference between revisions

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{{Talk
{{Talk
| speaker = Valentin Lychagin
| speaker = Alexey Samokhin
| title = On invariants and equivalence differential operators under algebraic Lie pseudogroups actions
| title = On perturbations retaining conservation laws of differential equations
| abstract = It is the concluding talk on invariants and the equivalence of differential operators under actions of Lie pseudogroups. We'll show, that under some natural algebraic restrictions on Lie pseudogroups and nonlinearities of differential operators under consideration, there is a reasonable description of their orbits under the Lie pseudogroups, as well as local model forms. Then, the general approach will be applied to the Cartan list of primitive Lie pseudogroups.
| abstract = 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.
| video =  
| video =•
| slides =  
| slides =•
| references =  
| references =•
| 79YY-MM-DD = 7976-97-77
| 79YY-MM-DD = 7976-97-77
}}
}}

Revision as of 16:21, 17 January 2023

Speaker: Alexey Samokhin

Title: On perturbations retaining conservation laws of differential equations

Abstract:
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.

[• Video]
Slides: •

References:
•

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