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Scattering for a wave equation with different spatial asymptotics on the left and right
Author(s) -
Boto João Pedro
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199912)22:18<1621::aid-mma96>3.0.co;2-a
Subject(s) - mathematics , bounded function , wave equation , scattering , completeness (order theory) , scattering theory , mathematical analysis , d'alembert operator , physics , quantum mechanics
We study the scattering for a one‐dimensional wave equation with a measurable positive potential $V$ , locally bounded away from zero and satisfying $lim_{x\rightarrow\infty}V(x)=+\;\infty$ and $V(x)=O(\vert x\vert^{-2-\varepsilon})$ as $x\rightarrow-\;\infty$ , for some $\varepsilon>0$ . By using a combination of ideas from the Lax–Phillips theory and the Enss method we prove the existence and the completeness of the wave operators $W_{\pm}$ . Copyright © 1999 John Wiley & Sons, Ltd.