Prev: Mapping the fruit fly brain
Next: Why There's So Much Pedophilia Re: Pedophile Priests
From: OsherD on 17 Apr 2010 10:03
From Osher Doctorow

Not only do sine and cosine convert to probabilities as in the last
few posts, but they are associated with Solitons which are "prototype"
undistorted waves. See Wikipedia's "Sine-Gordon Equation," "KdV
equation," and "Nonlinear Schrodinger Equation".

The Sine-Gordon Equation is:

1) Dtt(w) - Dxx(w) + sin(w) = 0, w = w(x, t)

It is 1-soliton and multi-soliton solutions among others, with:

2) w(x, t) = 4 arctan[exp(ma(x - vt) + b] with a^2 = 1/[1 - v^2]

and this has a quantum and SUSY extension. Arctangent increases with
tangent in one "cycle" (which we assume), but the key point is that
sin(w) in (1) yields the solitons.

The Nonlinear Schrodinger Equation does not have sin(w) in it, but it
does have |w|^2 which by the previous posts has a P(A) interpretation,
and is:

3) Dt(w) = -(1/2)Dxx(w) + k|w|^2 w, w = w(x, t)

with an exponential solution:

4) w = a exp(i theta) in water waves, with a = wave amplitude, arg(w)
= the phase theta

and with with a(xo, to), theta(xo, to) slowly-modulated amplitude and
phase and x and t linear functions of xo and to related to the group
velocity of the carrier wave.

The KdV equation does not have a P(A) related form overtly, but has a
sech^2 soliton solution (which of course is exponential related) of a
linear argument in x and t.

Osher Doctorow
 | 
Pages: 1
Prev: Mapping the fruit fly brain
Next: Why There's So Much Pedophilia Re: Pedophile Priests