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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| Format: | Article |
| Language: | English |
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Texas State University
2025-05-01
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| Series: | Electronic Journal of Differential Equations |
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| 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. |
| format | Article |
| id | doaj-art-ae5191ce7d914b5fbf2a748c14e34192 |
| 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 |