Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The solition and anti-solition nonlinear equation is given as:enter image description here

My problem is that, how do we get the next equation after considering asyptotic behaviour?

Resource: (solition) at page 38

share|improve this question
What is $\Delta$? Is $u$ related to $\bar{t}$ in any way? –  Antonio Vargas Aug 14 '13 at 21:06
Can you please check this book (users.ugent.be/~ddudal/sol&mon.pdf) at page 38? –  Complex Guy Aug 15 '13 at 19:14
I'm confused why you ask what $\Delta$ is. You yourself linked me to the pdf which says $$\Delta = ((1-u^2)/u)\ln u.$$ –  Antonio Vargas Aug 27 '13 at 20:00
Ohh my bad, then we just need to transform the hyperbolic term into exponential? –  Complex Guy Aug 27 '13 at 20:02
It seems plausible, but I haven't carried out the calculations. –  Antonio Vargas Aug 27 '13 at 20:03

1 Answer 1

This is due to the fact that: $$\lim_{x\to-\infty}\sinh(x) \sim -e^{-x}$$ And that: $$\cosh x =\frac{1}{2}e^{-x} + \frac{1}{2}e^x$$

share|improve this answer
Shouldn't that be $e^{-x}/2$? –  marty cohen Aug 31 '13 at 6:33
What will happen when you impose the $- \infty$? –  Complex Guy Aug 31 '13 at 10:58

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.