Boussinesq Solitons as Propagators of Neural Signals

Abstract

We  consider  certain  approximation for determining the  equation  of motion  for nerve  signals by  using  the  model  of the  lipid  melting  of membranes.   The  nerve  pulses  are  found  to  display nonlinearity and  dispersion  during  the  melting  transition.  In this  simplified model the  nonlinear equation  early  proposed  by  Heimburg  and  coworkers  transformed to  the  well known  integrable Boussinesq  non linear  equation.   Under  specific values of the  parametric space this  system  shows the  existence  of singular  and  regular  soliton  like structures.   After  their  collisions  the  mutual creation  and annihilation (each other)  of nerve signals along the  nerve,  during  their  propagation, has been observed.

Keywords: Boussinesq equation,  singular  solitons,  single neurons,  neural  code.