Solutions with expanding compact support of saturated Schr\"odinger equations: self-similar solutions
Abstract
We prove the existence of solutions \(u(t,x)\) of the Schr\"odinger equation with a saturation nonlinear term \((u/|u|)\) having compact support, for each \(t>0,\) that expands with a growth law of the type \(Ct\). The primary tool is considering the self-similar solution of the associated equation. For more information see https://ejde.math.txstate.edu/Volumes/2025/53/abstr.html
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