Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 282, Issue 10, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2022.109430
Keywords
Schrodinger equation; KAM tori; Quasi-periodic solutions
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Funding
- National Natural Science Foundation of China [11971012, 12001275, 12001276]
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In this study, a Whitney smooth family of small-amplitude quasi-periodic solutions is obtained in the two-dimensional nonlinear Schrödinger equation using an infinite dimensional KAM theorem.
We study the two-dimensional nonlinear Schrodinger equation iu(t) -Delta u + |u|(2)u partial derivative integral (x, u, u )/partial derivative u = 0, t is an element of R, x is an element of T-2 with periodic boundary conditions. The nonlinearity f (x, u, u) =Sigma(j,l,j+l >= 6) a(jl)(x)u(j)u, a(jl) = a(lj) is a real analytic function 6 in a neighborhood of the origin. We obtain, through an infinite dimensional KAM theorem, a Whitney smooth family of small-amplitude quasi-periodic solutions. (c) 2022 Elsevier Inc. All rights reserved.
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