Phenomenological Theory of Multimode Surface Wave Excitation Propagation And Di
Phenomenological Theory of Multimode Surface Wave Excitation Propagation And Di
Samuel Karp
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If we substitute ('i. 6) into (^.^3) and integrate by parts we obtain Up(x, y) in [h^^^(}'^_) - H^^^(kr^)] 2ni. \^(X^+XJ(X^+X^) ^2 1^^ 3 1^ \y 2niX^(X^- fXJ(X^^+X^) — (X _x ){x _x j ■ 1 23 2 •^oy ^i"! fi) e 1 H^l^(kR^)dTi r^ ^oT fl) C'. T) 2rtil (X +X )(X, ^+X ) -X^y ^. 1 3 ^ 3 2_il 3 3 / g 1 H;;"^(kR^)dTl rx -X )(x -X ) K 2_ 3-"^ 2 3^ ^' f \.^... This solution is not a wave function since the x-derivative in regions including the positive y-axis is discontinuous. We can remedy this defect, how...ever, by adding to (h.^) complementary solutions of the form -18- /"o 2~ /~2 ~ /~2 'c ^^y+i /k"+>^-L |xl -X^y + i/k +x; |x| ->^ y+i /k +1. Then u(x, y) = Up(x, y) +u^(x, y) (i+. 9) and the combined solution (4. 9) can be made to satisfy the continuity condition on -^ by suitably choosing the constants A^ A and A . We now determine 4^ from (i^-. T), (4. 8) and (4. Q), and substitute into (2. 14). We obtain tex (X +XJ(X +X ) -X y A = ^ ^ " ^--i- e ^ ° (4. 10) v5?'+^(V\K^-\) 4TCiX (X +X )(X +X ) -X^y^ /k^+X^ (X^.
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