H1-scattering for systems of N-defocusing weakly coupled NLS equations in low space dimensions*

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Cassano, B.¹  Tarulli, M.² 

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[2] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

关键词: Nonlinear Schrodinger systems;    Scattering theory;    Weakly coupled equations;   

DOI  :  10.1016/j.jmaa.2015.05.008

来源: Elsevier

【 摘 要 】

We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schradinger equations {i partial derivative(t)u(mu) +Delta u(mu) - Sigma(N)(mu,nu=1) beta(mu nu)vertical bar u(nu)vertical bar(p+1)vertical bar u(mu) = 0, mu = 1, ... , N, (u(mu)(0, center dot))(mu=1)(N) = (u(mu,0))(mu=1)(N) is an element of H-1 (R-d)(N), with N >= 2, beta(mu nu) >= 0, beta(mu mu) not equal 0 for p > 2 if d = 1, p > 1 if d = 2 and 1 <= p < 2 if d = 3. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free