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arXiv · 2506.04691

Solutions with expanding compact support of saturated Schr{\"o}dinger equations: self-similar solutions

Pascal Bégout·Jesus Ildefonso Diaz
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Abstract

We prove the existence of solutions \(u(t,x)\) of the Schr{\"o}dinger equation with a saturation nonlinear term \((u/|u|)\) having compact support, for each \(t>0,\) that expands with a growth law of the type \(C\sqrt{t}\). 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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Pascal Bégout, Jesus Ildefonso Diaz. 2025-06-05. Solutions with expanding compact support of saturated Schr{\"o}dinger equations: self-similar solutions. https://arxiv.org/abs/2506.04691

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