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 -