Phenomenological Theory of Multimode Surface Wave Excitation Propagation And Di

Cover 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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