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Unformatted text preview: ary conditions y ( ) = y ( ) = y ( 1 ) = y ( 1 ) . Why is there no loss of generality in not having a y 000 term in the equation? 4 The Helmholtz equation is 2 f + k 2 n 2 ( x ) f = , where k is a non-dimensional wavenumber and n ( x ) is a positive function. For large k , substitute the ansatz f = exp [ i k ( x )] n = A n ( x ) ( i k ) n into the equation and show that the equations satised by and A are | | 2 = n 2 , ( A 2 ) = . The former is called the eikonal equation while the latter is called the transport equation. 1...
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- Winter '08