To understand the solitary wave phenomenon it is necessary to appreciate the nature of a standing wave, a very nice example of which can be found here. There are 3 phases to be aware of.
1) the wave machine builds an oscillation, and the speed the wave moves combined with the wavelength synchronise to form a standing wave. The reflected wave builds on the incident wave to double the amplitude.
2) the machine is switched off and the synchronicity of the oscillation loses very little energy due to the lack of entropic or turbulent flow. The wave is sustained by gravity and dissipated through fluid viscosity and entropy.
3) as the wave dissipates it moves through a harmonic series, gradually releasing the stored energy into shorter wavelengths. The interference of the reflected wave kills the standing wave at half the wavelength.
Of note is the way the standing wave begins to "walk" up and down the channel moving in and out of phase. Also the later part of the video (after some time has elapsed in reality) the wavelets of the dissipating oscillation constitute only half the length of the tank, thus one quarter of the base harmonic, and the other half of the tank is relatively flat after it's passing.
The simplest example of a Solitary wave is where such a standing wave is allowed to freely exit into a shallower channel of water so that the speed of travel matches the energy dispersal through viscosity. The wave then moves as a single unit, maintaining its amplitude over some considerable distance and time. In fact even if such a channel opens out into a chaotic environment and deep water such as the sea, it will maintain its integrity moving as a unit, even exhibiting particle like behaviour. A solitary wave can bounce off an obstacle like a ball, or with a high enough energy can punch a hole through a surface like a bullet.
Of note is the way the standing wave begins to "walk" up and down the channel moving in and out of phase. Also the later part of the video (after some time has elapsed in reality) the wavelets of the dissipating oscillation constitute only half the length of the tank, thus one quarter of the base harmonic, and the other half of the tank is relatively flat after it's passing.
The simplest example of a Solitary wave is where such a standing wave is allowed to freely exit into a shallower channel of water so that the speed of travel matches the energy dispersal through viscosity. The wave then moves as a single unit, maintaining its amplitude over some considerable distance and time. In fact even if such a channel opens out into a chaotic environment and deep water such as the sea, it will maintain its integrity moving as a unit, even exhibiting particle like behaviour. A solitary wave can bounce off an obstacle like a ball, or with a high enough energy can punch a hole through a surface like a bullet.
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