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Título:
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Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations
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Autores:
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Begout, Pascal ;
Díaz Díaz, Jesús Ildefonso
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Tipo de documento:
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texto impreso
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Editorial:
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Department of Mathematics Texas State University, 2014
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Ecuaciones diferenciales
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Tipo = Artículo
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Resumen:
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“Sharp localized” solutions (i.e. with compact support for each given time t) of a singular nonlinear type Schrödinger equation in the whole space R N are constructed here under the assumption that they have a self-similar structure. It requires the assumption that the external forcing term satisfies that f(t, x) = t?(p?2)/2F (t?1/2x) for some complex exponent p and for some profile function F which is assumed to be with compact support in R N . We show the existence of solutions of the form u(t, x) = t p/2U(t?1/2x), with a profile U, which also has compact support in R N . The proof of the localization of the support of the profile U uses some suitable energy method applied to the stationary problem satisfied by U after some unknown transformation.
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En línea:
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https://eprints.ucm.es/id/eprint/29384/1/146.pdf
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