We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schrödinger equations{i∂tuμ+δuμ-∑μ,ν=1Nβμν|uν|p+1|uμ|p-1uμ=0,μ=1,. . .,N,(uμ(0,{dot operator}))μ=1N=(uμ,0)μ=1N∈H1(Rd)N, with N≥2, βμν≥0, βμμ≠0 for p>2 if d=1, p>1 if d=2 and 1≤p<2 if d=3.
H1-scattering for systems of N-defocusing weakly coupled NLS equations in low space dimensions
Cassano B.;
2015-01-01
Abstract
We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schrödinger equations{i∂tuμ+δuμ-∑μ,ν=1Nβμν|uν|p+1|uμ|p-1uμ=0,μ=1,. . .,N,(uμ(0,{dot operator}))μ=1N=(uμ,0)μ=1N∈H1(Rd)N, with N≥2, βμν≥0, βμμ≠0 for p>2 if d=1, p>1 if d=2 and 1≤p<2 if d=3.File in questo prodotto:
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