2026-06-01T02:29:30Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/339502023-08-28T17:47:50Zcom_20.500.14352_14col_20.500.14352_15

Self-similar solutions with compactly supported profile of some nonlinear Schrödinger equations Bègout, Pascal Díaz Díaz, Jesús Ildefonso 517.9 Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias “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. Unión Europea. FP7 DGISPI UCM Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:31:52Z 2023-06-19T13:31:52Z 2014 journal article https://hdl.handle.net/20.500.14352/33950 1072-6691 eng FIRST (238702) MTM2011-26119 Group MOMAT (910480) open access application/pdf Department of Mathematics Texas State University