# Samokhin A. Conservation laws in action: an approach and implementations (abstract)

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**Speaker**: Alexey Samokhin

**Title**: Conservation laws in action: an approach and implementations
**Abstract**:

Quantities which are conserved in nondissipative media decay in presence of dissipation. The selective rates of such a decay can be found explicitly using the generating functions of the conservation laws. The general approach is illustrated by three examples:

- An arbitrary compact-support initial datum for the KdV equation eventually splits into solitons and a radiation tail. A numerically simple method to predict the number and amplitudes of resulting solitons using only a finite number of conservation laws is given.
- The behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or dispersion; beyond the layer dispersion is constant (but not necessarily of the same value) and dissipation is null. The passed wave either retains the form of a soliton or becomes a multi-soliton. Some rough estimations for a prediction of an output are given using the selective decay of the KdV conserved quantities.
- Some solutions of a system of MHD-equations for incompressible magnetofluids are found using the selective decay and the Taylor trick.

**Event:** Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.*Alexandre Vinogradov Memorial Conference.*