Time evolution of the action potential in plant cells

In this paper we extend and reconsider a solitonic model of the actionpotential in biological membranes for the case of plant cells. Aiming togive at least a qualitative description of the K(+),Cl(-) and Ca(2+) driven process of propagation ofthe action potential along plant cells we put forward the hypothesis ofthree scalar fields φ(i) (X), i = 1, 2, 3 which representK(+), Cl(-) and Ca(2+) ions,respectively. The modulus squared of these fields carries the usualquantum-mechanical (probabilistic) interpretation of the wave function. Onthe other hand, the fields are described themselves by the Lagrangiandensities ℒ[Formula: see text]. Moreover, the interaction and self-interaction term ℒ[Formula: see text] between thefields is considered. The Lagrangian densities ℒ[Formula: see text]include a double-well potential (which is proportional toσ(4) (i)) that leads to spontaneous symmetrybreaking which may produce structures with non-zero topological charge, e.g.longitudinal solitons. In order to describe the transversal motion of theions of concern we need to assume only non-uniform solutions of the system of equation of motion. Hence we seek for solutions (travelling waves) whichpreserve the shape and which move without dissipation and in this way wereconstruct the main dynamical features of the action potential in plants.