Journal Articles Electronic Journal of Differential Equations Year : 2025

Solutions with expanding compact support of saturated Schrödinger equations: self-similar solutions

Abstract

We prove the existence of solutions \(u(t,x)\) of the Schrödinger 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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hal-05091562 , version 1 (01-06-2025)

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Pascal Bégout, Jesus Ildefonso Diaz. Solutions with expanding compact support of saturated Schrödinger equations: self-similar solutions. Electronic Journal of Differential Equations, 2025, 2025 (53), pp.01-15. ⟨10.58997/ejde.2025.53⟩. ⟨hal-05091562⟩
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