sech

Well, then, what kind o' brothers would it be that 'd stand in his way at sech a time?

March bein' told, and worried just for sech a trifle.'

"The falls has been there sence the beginnin' o' time, an' I cal'late they'll be there till the end on 't; so you needn't 'a' been in sech a brash to git a sight of 'em.

I know'd in my mind, as he'd have told her wonders of 'em, and how she was to be a lady theer, and how he got her to listen to him fust, along o' sech like.

'Aye, and bloomin' glad they'll be to see us there.' Did I not say to you that the lady had a noble 'art, and would show it when put to the test by sech a calamity as this?"

Which I meantersay as sech if you're a man, come on!

First, [a.sub.0] = sech(0) = 1 and [a.sub.1] = sech'(0) = 0 are substituted in the right-hand-side of the last equation.

The sech shape typical for solitons is mathematically less convenient than a Gaussian: an initially Gaussian pulse, upon dispersion, remains Gaussian everywhere, except for rescaling, but underneath the Gaussian envelope a linear chirp (quadratic phase profile) develops.

Seeking the solution by sech function method as in (6)

[[rho].sub.0] (t) = [+ or -] [cube root of 2w/[sigma]] sech ([square root of 19/8]wt).