{"title":"Scattering Theory for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions","authors":"A. Shimomura","doi":"10.14492/hokmj/1285766230","DOIUrl":null,"url":null,"abstract":"We study the scattering theory for the coupled Klein- Gordon-Schrodinger equation with the Yukawa type interaction in two space dimensions.The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state. 2 . (KGS) Here u and v are complex and real valued unknown functions of (t, x) ∈ R × R 2 , respectively.In the present paper, we prove the existence of the wave operators to the equation (KGS) without any size restriction on the Klein-Gordon component of the final state. A large amount of work has been devoted to the asymptotic behavior of solutions for the nonlinear Schrodinger equation and for the nonlinear Klein- Gordon equation.We consider the scattering theory for systems centering on the Schrodinger equation, in particular, the Klein-Gordon-Schrodinger, the Wave-Schrodinger and the Maxwell-Schrodinger equations.In the scat- tering theory for the linear Schrodinger equation, (ordinary) wave operators","PeriodicalId":50143,"journal":{"name":"Journal of Mathematical Sciences-The University of Tokyo","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2005-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Sciences-The University of Tokyo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.14492/hokmj/1285766230","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 18
Abstract
We study the scattering theory for the coupled Klein- Gordon-Schrodinger equation with the Yukawa type interaction in two space dimensions.The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state. 2 . (KGS) Here u and v are complex and real valued unknown functions of (t, x) ∈ R × R 2 , respectively.In the present paper, we prove the existence of the wave operators to the equation (KGS) without any size restriction on the Klein-Gordon component of the final state. A large amount of work has been devoted to the asymptotic behavior of solutions for the nonlinear Schrodinger equation and for the nonlinear Klein- Gordon equation.We consider the scattering theory for systems centering on the Schrodinger equation, in particular, the Klein-Gordon-Schrodinger, the Wave-Schrodinger and the Maxwell-Schrodinger equations.In the scat- tering theory for the linear Schrodinger equation, (ordinary) wave operators
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