File:Eckhaus equation wave packet.gif
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Eckhaus_equation_wave_packet.gif (480 × 96 pixels, file size: 626 KB, MIME type: image/gif, looped, 301 frames, 8.0 s)
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[edit]DescriptionEckhaus equation wave packet.gif | Animation of a wave-packet solution of the Eckhaus equation. The blue line is the real part of the solution, the red line is the imaginary part, the black line is the wave envelope (absolute value) and the green line is the centroid of the wave packet envelope. |
Date | |
Source | Own work |
Author | Kraaiennest |
Other versions | File:Schrödinger equation wave packet.gif gives an animation of the corresponding solution of the linear Schrödinger equation. |
Background InfoField | The Eckhaus equation is with while and denote the one-dimensional space and time coordinates, respectively. The Eckhaus equation can be linearized to the linear Schrödinger equation as follows: for a certain – which is a solution to the linear Schrödinger equation – the corresponding solution to the Eckhaus equation is:
The wave-packet solution used here (to the linear Schrödinger equation) is: with the group velocity and the amplitude. This solution has an envelope of Gaussian shape: So the envelope of the linear solution widens with time, and becomes lower. Further with erf the error function. The centre of gravity of the wave packet is computed as The shown animation is for an amplitude and group velocity Note the asymmetry in the envelope for the Eckhaus equation, while the envelope – of the corresponding solution to the linear Schrödinger equation – is symmetric (in ). The short waves in the packet propagate faster than the long waves. |
This diagram was created with MATLAB.
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[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 09:18, 6 September 2014 | 480 × 96 (626 KB) | Kraaiennest (talk | contribs) | including the propagation of the centre of gravity | |
22:54, 4 September 2014 | 480 × 96 (595 KB) | Kraaiennest (talk | contribs) | Smaller size | ||
21:38, 4 September 2014 | 640 × 120 (875 KB) | Kraaiennest (talk | contribs) | == {{int:filedesc}} == {{Information |Description=Animation of a wave-packet solution of the Eckhaus equation. |Source={{Own}} |Date=2014-09-04 |Author= Kraaiennest |Permission= |other_v... |
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