Pascal Begout, Jesus Ildefonso Diaz
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 \(C\sqrt{t}\).
The primary tool is considering the self-similar solution of the associated
equation.
Submitted April 14, 2025. Published May 24, 2025.
Math Subject Classifications: 35C06, 35A01, 35A02, 35J91, 35Q55.
Key Words: Schrodinger equation with saturated nonlinearity;
solutions compactly supported; energy method; Dirichlet boundary condition;
Neumann boundary condition; existence; uniqueness.
DOI: 10.58997/ejde.2025.53
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Pascal Bégout Toulouse School of Economics, Université Toulouse Capitole Institut de Mathématiques de Toulouse 1, Esplanade de l'Université 31080 Toulouse Cedex 6, France email: Pascal.Begout@math.cnrs.fr, ORCID: 0000-0002-9172-3057 |
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Jesús Ildefonso Díaz Instituto de Matemática Interdisciplinar Universidad Complutense de Madrid Plaza de las Ciencias, 3 28040 Madrid, Spain email: jidiaz@ucm.es, ORCID: 0000-0003-1730-9509 |
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