Asymptotic Expansions of Solutions of Initial Boundary Value Problems for a Disp
Asymptotic Expansions of Solutions of Initial Boundary Value Problems for a Disp
Norman Bleistein
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A solution of (lO) is (11) W(^, +U)) = R_^ E-(4) vhere 00 (12) E-(^) = J expfi 2i^^Jd^ i We note that R_^ and 4 are functions of to. It can be shown that when this function is substituted into (lU), v^ satisfies the radiation condition. 33 Therefore, if R are chosen so as to make W satisfy the boundary condition, (3), v^ will be determined. From (3)> (7) and (ll), it follows that (13) R^= -Mjy)[EH\x kpJ^/^A - L J Using (11), (12) and (13) in (2), we obtain (1^) Vj^(X, +uj) = -A(4<. f="" fig.="" ray="" picture="" in="" space="" for="" the="" case="" of="" rapidly="" varying="" initial="" data.="" projection="" rays="" space.="">-! ^ n H- ...<. f="" fig.="" ray="" picture="" in="" space="" for="" the="" case="" of="" rapidly="" varying="" initial="" data.="" projection="" rays="" space.="">C Oq ►-i
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