For the saturated nonlinear Schrödinger equation, self-similar solutions with compact support expanding like C√t exist when the self-similar forcing is small and decays outside a compact set.
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Solutions with expanding compact support of saturated Schr{\"o}dinger equations: self-similar solutions
For the saturated nonlinear Schrödinger equation, self-similar solutions with compact support expanding like C√t exist when the self-similar forcing is small and decays outside a compact set.