Analytic and Numerical Solutions to Nonlinear Partial Differential Equations in Biomechanics

摘要: The study of exact solutions to nonlinear equations is an active field of both, pure and applied mathematics. Plenty of the most interesting features of physical systems are hidden in their nonlinear behavior and can only be studied with appropriate methods designed to tackle nonlinearity. Therefore, seeking for suitable solving methods, exact, semi-exact or numerical, is an active task in branches of applied and computational mathematics. Complex phenomena in notable scientific fields, especially in physics, such as fluid and plasma dynamics, optical fibers, solid state physics, as well as in cardiac hemodynamics, can be efficiently mathematically modeled in terms of the Korteweg–de Vries (KdV), modified KdV (mKdV), Burgers and Korteweg–de Vries–Burgers (KdV–B) equations. In this review chapter, analytical solutions are sought for each of the aforementioned equations, by means of traveling wave and …