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Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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Linear quantization in quantum electrodynamics?

This is a continuation of this question. What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.