The Solution of a Certain Nonlinear Riemann Hilbert Problem With An Application
The Solution of a Certain Nonlinear Riemann Hilbert Problem With An Application
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5). We find (4. 14) F+(C)F~(C)+ '^^^^•' l^^^^^ [F'^(C) + F-(C)] +1 = 0.
The pair (4. L4) and either (4. 4) or (4. 5), is equivalent to (4. 4) and (4. 5).
Since (4. 2) is in force, we know from Section 3 and (3. 16) that if (4. 15) A(w) ^yiw-aj(w-pj r ^^ U-a(zjJ "2?r "1+ a(z) ^ (z-w)/(z-aj(z-Pj dz, where [1+ a(z )]/[l - a(z)] neither vanishes nor becomes infinite for z on L, then 20 p2A(w) (4. 16) F-l(w) = \^^^^ = coth A(w) is a particular solution of (4. L4). From this, we find by substituting ...Xi(^) = Fi(w)x2(w) in (4. 4) and (4. 5), that Xo(^) ni^st [p^(c). MiN^(i)ijtx^(c)]2 (4. 17) Equation (4. L4) shows that (, . , 8) Mc)-a(o_t^l(c)p-, (0. Ii ^ F+(0 + F-{C) and therefore equation (4. 17) is the same as (4. 19) [[F^(c)]^- ii[x2(c)]^- li^liof- ihxliof = The function (4. 20) X2^^) " "^ = sinh A(w) jpfM -1 satisfies (4. 19); it is analytic in D and behaves like a constant at infinity. Corresponding to this Xo^^^' ^^^ function Xi (^) i^ (4. 21) Xi(^) = Fj_(w)x2(w) = cosh A(w) 21 and it also satisfies the original conditions imposed on )(-, and y^ by being analytic in D and behaving like a constant at infinity.
What to read after The Solution of a Certain Nonlinear Riemann Hilbert Problem With An Application?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
5). We find (4. 14) F+(C)F~(C)+ '^^^^•' l^^^^^ [F'^(C) + F-(C)] +1 = 0.
The pair (4. L4) and either (4. 4) or (4. 5), is equivalent to (4. 4) and (4. 5).
Since (4. 2) is in force, we know from Section 3 and (3. 16) that if (4. 15) A(w) ^yiw-aj(w-pj r ^^ U-a(zjJ "2?r "1+ a(z) ^ (z-w)/(z-aj(z-Pj dz, where [1+ a(z )]/[l - a(z)] neither vanishes nor becomes infinite for z on L, then 20 p2A(w) (4. 16) F-l(w) = \^^^^ = coth A(w) is a particular solution of (4. L4). From this, we find by substituting ...Xi(^) = Fi(w)x2(w) in (4. 4) and (4. 5), that Xo(^) ni^st [p^(c). MiN^(i)ijtx^(c)]2 (4. 17) Equation (4. L4) shows that (, . , 8) Mc)-a(o_t^l(c)p-, (0. Ii ^ F+(0 + F-{C) and therefore equation (4. 17) is the same as (4. 19) [[F^(c)]^- ii[x2(c)]^- li^liof- ihxliof = The function (4. 20) X2^^) " "^ = sinh A(w) jpfM -1 satisfies (4. 19); it is analytic in D and behaves like a constant at infinity. Corresponding to this Xo^^^' ^^^ function Xi (^) i^ (4. 21) Xi(^) = Fj_(w)x2(w) = cosh A(w) 21 and it also satisfies the original conditions imposed on )(-, and y^ by being analytic in D and behaving like a constant at infinity.
What to read after The Solution of a Certain Nonlinear Riemann Hilbert Problem With An Application?
You can find similar books in the "Read Also" column, or choose other free books by Arthur S Peters to read onlineMoreLess
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