Heat solitons and thermal transfer of information along thin wires

Abstract

The aim of this paper is to consider soliton propagation of heat signals along a cylinder whose heat exchange with the environment is a non-linear function of the difference of temperatures of the cylinder and the environment and whose heat transfer along the system is described by the Maxwell–Cattaneo equation. To find the soliton solutions we use the auxiliary equation method. Our motivation is to obtain and compare the speed of propagation, the maximum rate of information transfer, and the energy necessary for the transfer of one bit of information for different solitons, by assuming that a localized soliton may carry a bit of information. It is shown that a given total power (energy/time) may be used either to send a few bits in a fast way, or many bits in a slower way. This may be controlled by choosing the initial condition imposed at one end of the wire.