can some one tell me how to find values of si1(0) and si1(1) usng matlab?
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Walter Roberson
on 13 Jan 2017
Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions, by Boling Guo, Liming Ling, and Q. P. Liu
Accepted Answer
Walter Roberson
on 8 Jan 2017
taylor() can only be used for functions whose differentiation can be evaluated at the point of expansion.
Your expression has a denominator of sqrt(h^2-1) which is a problem if h is 1. You have h = 1 + f^2 so that is equal to 1 when f is 0. Therefore your expression has a division by 0 at f = 0. Such a function has no taylor expansion.
You can create a series() expansion of X1 around f = 0, but it will not look like what they show, and furthermore for the same reason the series does not really exist at 0. The expression involves csgn(), the Complex Sign operator, and a division by f; if you restrict to real valued f (we cannot read the image well enough to tell if that is justified) then you end up with signum(f)/f and then you have the question of what signum(0) is. You could potentially rewrite the signum(f)/f in terms of abs(), in which case it comes out as 1/abs(f), which gives you a leading term of
-(1/2)*exp(-(1/2*I)*t)*sqrt(2)*(-i+I)/abs(f)
Perhaps everything except for the abs(f) could be rewritten to look like what they wrote, but the abs(f) cannot be eliminated.
Your C1 has a limit of infinity near h = 1 and there really is no way around that: any expansion around that point is going to be infinite.
You could potentially expand around f = epsilon instead of around f = 0, and then take the limit as epsilon approaches 0... but the limit does not exist.
Either you have made a typing mistake or else they describe something that we viewers cannot read (the image quality is poor), or else what they describe is incorrect.
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