Traveling‐wave solutions for a nonlinear non‐Ohmic cardioelectrophysiological tissue conduction cable equation

Abstract

In this article, families of solitary waves solutions of a general third‐order nonlinear non‐Ohmic cable equation in cardio‐electro‐physiology are obtained using the ‐expansion method. In this equation, the unknown function represents the trans‐membrane current, and the exact soliton‐like solutions are thoroughly derived using this analytic technique, and illustrated through surface and contour plots. To support the analytical findings presented in this work, the existence of solution and their optimal regularity is proved rigorously using Shauder's fixed‐point theorem.