The name is absent

Following the Q-mind hypothesis we further could suggest that positive or
negative quasiparticles known as solitons could transfer energy between the
tubulin tails without dissipation. The solitons are nonlinear waves that do not
disperse as they propagate (Dodd et al., 1982; Fordy, 1994) and include kinks,
antikinks and different kind of breathers (Dmitriev et al., 1997; 1998a; 1998b;
2000; Miroshnichenko et al., 2000).

We could adopt subneuronal computation in brain microtubules via solitons that
are localized excitations propagating in a system with constant velocity and
colliding with each other without change in their shapes. During the collision of
solitons the solution cannot be represented as a linear combination of two soliton
solutions but after the collision solitons recover their shapes and the only result of
collision is a phase shift. There are several equations whose solutions produce
solitons (Wadati, 2001). One of the best studied is the sine-Gordon model
described by Lagrangian:

1∂²φ(x,t)   1∂²φ(x,t)

(110)             L = ^-⅛^, -ɔ     2^,  - (1 - cosΦ(x, t))

2∂t²2∂x²

There are known static solutions to the sine-Gordon model:

(111)              φ = 4 arctan e^x

(112)              φ = 4 arctan e^-x

that have winding numbers 1 and -1, respectively. The first solution is known as
kink and the second as anti-kink. The kink is an exponentially localized lump of
energy centered around x = 0. Other static solutions can be obtained by
translating this solution and moving solutions can be obtained by Lorenz
transform. Two of these kinks at different positions can be superimposed and
allowed to evolve, they will move away from each other (Houghton, 2000).

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