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 'Mechanism of Energy Conservation in Zero-Amplitude Sum of EM Waveforms'

Assume that this is a case where by sheer coincidence, two sources of coherent single-frequency EM wave pulses with equal duration are both fired in opposing directions, with both carrying the same frequency and amplitude and orientation. These two waves meet head-on while moving in opposing directions, and their phases are precisely offset by 180 degrees so that each trough of one wave meets with the crest of the other. This should be true for both the electric and magnetic components of...
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