Plasma Approach to Describing the Electric Dynamics of a Neuron

The electric excitation of a neuron is interpreted as the formation of a nonlinear solitary ion acoustic wave of the charge density of sodium and hydrogen ions in an electrolytic intracellular fluid, which is treated as a dense plasma. It is shown that such a wave can be described by the coupled sine-Gordon and Korteweg–de Vries equations, having a solution in the form of a soliton whose internal vibrational structure is described by the Fermi–Pasta–Ulam spectrum. It is concluded that a nerve impulse can be interpreted as a low-frequency solitary wave of the charge density of sodium ions with a trapped high-frequency charge density wave of protons.