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

We prove the existence of solutions $u(t,x)$ of the Schrodinger 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 equat...

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Main Authors: Pascal Begout, Jesus Ildefonso Diaz
Format: Article
Language:English
Published: Texas State University 2025-05-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2025/53/abstr.html
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author Pascal Begout
Jesus Ildefonso Diaz
author_facet Pascal Begout
Jesus Ildefonso Diaz
author_sort Pascal Begout
collection DOAJ
description We prove the existence of solutions $u(t,x)$ of the Schrodinger 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.
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institution Kabale University
issn 1072-6691
language English
publishDate 2025-05-01
publisher Texas State University
record_format Article
series Electronic Journal of Differential Equations
spelling doaj-art-ae5191ce7d914b5fbf2a748c14e341922025-08-20T03:46:36ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-05-01202553,115Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutionsPascal Begout0Jesus Ildefonso Diaz1 Univ. Toulouse Capitole, France Univ. Complutense de Madrid, Spain We prove the existence of solutions $u(t,x)$ of the Schrodinger 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.http://ejde.math.txstate.edu/Volumes/2025/53/abstr.htmlschrodinger equation with saturated nonlinearitysolutions compactly supportedenergy methoddirichlet boundary conditionneumann boundary conditionexistenceuniqueness
spellingShingle Pascal Begout
Jesus Ildefonso Diaz
Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
Electronic Journal of Differential Equations
schrodinger equation with saturated nonlinearity
solutions compactly supported
energy method
dirichlet boundary condition
neumann boundary condition
existence
uniqueness
title Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
title_full Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
title_fullStr Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
title_full_unstemmed Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
title_short Solutions with expanding compact support of saturated Schrodinger equations: self-similar solutions
title_sort solutions with expanding compact support of saturated schrodinger equations self similar solutions
topic schrodinger equation with saturated nonlinearity
solutions compactly supported
energy method
dirichlet boundary condition
neumann boundary condition
existence
uniqueness
url http://ejde.math.txstate.edu/Volumes/2025/53/abstr.html
work_keys_str_mv AT pascalbegout solutionswithexpandingcompactsupportofsaturatedschrodingerequationsselfsimilarsolutions
AT jesusildefonsodiaz solutionswithexpandingcompactsupportofsaturatedschrodingerequationsselfsimilarsolutions