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.