Title: The Nonlinear Schrödinger Equation for the Description of
Mechanical Changes in Phase with the Action Potential in Neurons
Abstract: In this work we show that, using the reductive
perturbation method, an action potential, considered as a carrier wave
modulation propagating in a neuronal axon, may be described by the
Nonlinear Schrödinger Equation (NLS). ÊBy modeling the neuronal axon as a
fluid-filled elastic tube composed of elastic rings we also propose that
the localized pressure increase in the fluid (Soliton) causes a radially
symmetric expansion of the elastic rings in the region of the pressure
increase, which is consistent with the experimental observations carried
out quite recently by Gonzalez et al., (submitted 2016), who found that
mechanical changes in the axon membrane i.e. a swelling of a few nm occur
in phase with the action potentials. The novel soliton solutions of the
NLS model are being explored in order to describe phenomena occurring in
neurons such as pulse attraction-repulsion recently observed (Villagran et
al., 2013). We also discuss the possibility to apply this model
to neural networks in order to describe both the probability of pulse
transmission to the postsynaptic neuron and the Êaction potential
back-propagation.