TY - JOUR
T1 - On a system of nonlinear Schrödinger equations with quadratic interaction
AU - Hayashi, Nakao
AU - Ozawa, Tohru
AU - Tanaka, Kazunaga
PY - 2013
Y1 - 2013
N2 - We study a system of nonlinear Schrödinger equations with quadratic interaction in space dimension n≤6. The Cauchy problem is studied in L 2, in H1, and in the weighted L2 space 〈 x〉-1L2=F(H1) under mass resonance condition, where 〈x〉=( 1+|x|2)1/2 and F is the Fourier transform. The existence of ground states is studied by variational methods. Blow-up solutions are presented in an explicit form in terms of ground states under mass resonance condition, which ensures the invariance of the system under pseudo-conformal transformations.
AB - We study a system of nonlinear Schrödinger equations with quadratic interaction in space dimension n≤6. The Cauchy problem is studied in L 2, in H1, and in the weighted L2 space 〈 x〉-1L2=F(H1) under mass resonance condition, where 〈x〉=( 1+|x|2)1/2 and F is the Fourier transform. The existence of ground states is studied by variational methods. Blow-up solutions are presented in an explicit form in terms of ground states under mass resonance condition, which ensures the invariance of the system under pseudo-conformal transformations.
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U2 - 10.1016/j.anihpc.2012.10.007
DO - 10.1016/j.anihpc.2012.10.007
M3 - Article
AN - SCOPUS:84881164350
SN - 0294-1449
VL - 30
SP - 661
EP - 690
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -