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International Journal of Mathematics and Mathematical Sciences - Volume 29 2002, Issue 9, Pages 501-516



Department of Mathematics, Graduate School of Science, Osaka University, Osaka 560-0043, Japan

Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 Xangari, Morelia, Michoacán CP 58089, Mexico

Received 15 February 2001; Revised 20 May 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study asymptotic behavior in time of global small solutions tothe quadratic nonlinear Schrödinger equation intwo-dimensional spaces i∂tu+1-2Δu=and#x1D4A9;u, t,x∈ℝ×ℝ2;u0,x=φx, x∈ℝ2, where and#x1D4A9;u=Σj,k=12λjk∂xju∂xku+μjk∂xju¯∂xku¯, whereλjk,μjk∈ℂ. We prove that if the initial dataφ satisfy some analyticity and smallness conditions in asuitable norm, then the solution of the above Cauchy problem hasthe asymptotic representation in the neighborhood of thescattering states.





Autor: Nakao Hayashi and Pavel I. Naumkin

Fuente: https://www.hindawi.com/



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