The Inverse Scattering Problem
The Inverse Scattering Problem
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In our eReader you can find the full English version of the book. Read The Inverse Scattering Problem Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Inverse Scattering Problem
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3 )♦ Further, a solution u(k, x) of (2. 1) is given by (3. 2) when u (k, x) satisfies (3»l). The function u(k, x) given by (3. 2) is evidently continuous, and because K(x, y) is continuous and partial derivatives of K(x, y) are piecewise continuous, u(k, x) has a continuous derivative.
For the second part of the proof we must show that the solution of (2. 1) given by (3. 2) when u^(k, x) - e^^ + b(x) e"^*"' is the one which has ikx the behavior u(k, x) ~ a(k) e for x -»• +oo. It is difficult to... ascertain directly the behavior as x -»- +oo of a solution u(k, x) of (2. 1) when u(k, x) is given in the form (3. 2), but its behavior as x -»• -oo is just u (k, x). We shall therefore investigate the character of our solution u(k, x), which aj>- preaches e +b(k) e as x -► -oo, by comparing it with that (unique) solution u(k, x) of (2. 1) iirtiich has the behavior e~ as x -»• -oo. We know: if and only if (U. 6) i / u(k, x) u(k, y) dk - 5(x-y), u(k, x) has the behavior (U. 7) u(k, x).
What to read after The Inverse Scattering Problem?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3 )♦ Further, a solution u(k, x) of (2. 1) is given by (3. 2) when u (k, x) satisfies (3»l). The function u(k, x) given by (3. 2) is evidently continuous, and because K(x, y) is continuous and partial derivatives of K(x, y) are piecewise continuous, u(k, x) has a continuous derivative.
For the second part of the proof we must show that the solution of (2. 1) given by (3. 2) when u^(k, x) - e^^ + b(x) e"^*"' is the one which has ikx the behavior u(k, x) ~ a(k) e for x -»• +oo. It is difficult to... ascertain directly the behavior as x -»- +oo of a solution u(k, x) of (2. 1) when u(k, x) is given in the form (3. 2), but its behavior as x -»• -oo is just u (k, x). We shall therefore investigate the character of our solution u(k, x), which aj>- preaches e +b(k) e as x -► -oo, by comparing it with that (unique) solution u(k, x) of (2. 1) iirtiich has the behavior e~ as x -»• -oo. We know: if and only if (U. 6) i / u(k, x) u(k, y) dk - 5(x-y), u(k, x) has the behavior (U. 7) u(k, x).
What to read after The Inverse Scattering Problem?
You can find similar books in the "Read Also" column, or choose other free books by Irvin W Kay to read onlineMoreLess
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