A Stretching Coordinates System/Reductive perturbation theory

Ahmer ali
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why stretching coordinate transformation is used in the study of solitons formation using reductive perturbation theory?
What is the physical reason behind the usually used transformation of the form mentioned below
transformation.JPG
 
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Thread 'The Physics of unloading sand from a barge'

I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...
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