 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12977 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8096
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| In English (Mech. Solids): | | 4881 |
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| S.A. Shcherbinin, "Dynamics of the Energy Center of a Long-Wave Low-Amplitude Disturbance in an Anharmonic One-Dimensional Lattice," Mech. Solids. 59 (5), 3235-3243 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
5 |
Pages |
3235-3243 |
| DOI |
10.1134/S0025654424606001 |
| Title |
Dynamics of the Energy Center of a Long-Wave Low-Amplitude Disturbance in an Anharmonic One-Dimensional Lattice |
| Author(s) |
S.A. Shcherbinin (Peter the Great St. Petersburg Polytechnical University, St. Petersburg, 195251 Russia;Institute for Problems in Mechanical Engineering RAS, St. Petersburg, 199178 Russia, stefanshcherbinin@gmail.com) |
| Abstract |
The dynamics of a disturbance with finite energy in an infinite monatomic nonlinear one-dimensional lattice are analyzed. Based on the energy dynamics approach proposed earlier, we focus
on such disturbance spatial characteristic as the position of its energy center. Restricting our analysis
to long-wave low-amplitude disturbances, we investigate the dynamics of the α-FPU chain using its continuous version described by the KdV equation. We establish a connection of the Lagrangian and
the energy of the original chain with the two conserving quantities of the KdV equation. Using these
two quantities and the known properties of the KdV equation, we propose a method for determining the velocity of the energy center of the disturbance at large times based on the initial conditions. |
| Keywords |
energy transfer, KdV equation, solitons, energy dynamics approach |
| Received |
28 October 2024 | Revised |
07 November 2024 | Accepted |
08 November 2024 |
| Link to Fulltext |
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