二维耦合Klein-Gordon-Schrödinger方程的散射理论

Q3 Mathematics

Journal of Mathematical Sciences-The University of Tokyo Pub Date : 2005-06-01 DOI:10.14492/hokmj/1285766230

A. Shimomura

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引用次数: 18

摘要

研究了二维空间中具有汤川型相互作用的Klein- Gordon-Schrodinger耦合方程的散射理论。该方程的散射问题属于近程和远距离的交界点。我们证明了该方程的波动算子的存在性，而对最终态的Klein-Gordon分量没有任何大小限制。2 ． (KGS)这里u和v分别是(t, x)∈R × r2的复实值未知函数。在本文中，我们证明了方程(KGS)的波动算子的存在性，而最终态的Klein-Gordon分量没有任何大小限制。对于非线性薛定谔方程和非线性Klein- Gordon方程解的渐近性，人们做了大量的研究工作。我们考虑了以薛定谔方程为中心的系统散射理论，特别是Klein-Gordon-Schrodinger、Wave-Schrodinger和Maxwell-Schrodinger方程。在线性薛定谔方程的散射理论中，(普通)波算符

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Scattering Theory for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions

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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来源期刊

Journal of Mathematical Sciences-The University of Tokyo 数学-数学

CiteScore

0.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： La política de la Revista de Ciencias Matemáticas de la Universidad de Tokio es publicar trabajos de investigación originales en las ciencias matemáticas, incluidas las matemáticas puras y aplicadas. Además, también es nuestra política publicar la revista en formato impreso, así como electrónicamente en Internet. Precisamente hablando, los manuscritos de más de un año están disponibles en nuestra página de inicio en formato PDF.